id
stringlengths 26
62
| setting_key
stringclasses 41
values | messages
listlengths 1
1
| ground_truth
stringlengths 1
9
| dataset
stringclasses 1
value | omega_config
stringclasses 41
values | omega_split
stringclasses 2
values |
|---|---|---|---|---|---|---|
algebra_func_area_test_out_000
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-1(3|(-2x - 5)| - 1) + 1)/(-3(3|(-2x - 5)| - 1)) and g(x) = 3cos(3π((1x + 3)/(-2x - 1)) - 3) - 2 from x = 0.0 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.5
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_001
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2|(3((2(3x^2 - 5x + 1) - 3)/(2(3x^2 - 5x + 1) + 3)) - 4) + 1| - 1, g(x) = 2e^(1(5(-3|x| + 3) - 2)) + 1, x = 0.7, and x = 2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
22.1
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_002
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3|(1(1cos(1π(-1x - 3) + 1) + 1)^2 - 5(1cos(1π(-1x - 3) + 1) + 1) + 4) - 1| + 1, g(x) = 5((-2(-4x) - 1)/(1(-4x) + 2))^2 - 5((-2(-4x) - 1)/(1(-4x) + 2)) - 5, x = -0.1, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.7
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_003
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1(3sin(3π(3(1x^2 - 5x + 4) + 1) - 1) - 3) - 3)/(-2(3sin(3π(3(1x^2 - 5x + 4) + 1) - 1) - 3) - 2), g(x) = -2(-2|((-3x - 2)/(-3x - 1)) + 3| - 2) - 5, x = -4.0, and x = -3.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.5
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_004
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(1π(1(2|(-2((2x - 3)/(2x - 1))^2 - 1((2x - 3)/(2x - 1)) - 1) + 2|) - 2) + 1) + 3 and g(x) = -2cos(1π(5(-1|((-2x - 3)/(-1x - 2)) - 1| - 2) + 2) + 3) + 2 between the vertical lines x = -2.0 and x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_005
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2((-1(2e^(-1x)) - 2)/(2(2e^(-1x)) + 1)) + 4 and g(x) = -3(-3|x + 1|)^2 - 3(-3|x + 1|) + 4 from x = -1.4 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.3
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_006
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(1(-2|x| - 3) - 5) - 2)/(-1(1(-2|x| - 3) - 5) - 1) and g(x) = -4(-1|x - 1| + 3) - 2 between the vertical lines x = -1.6 and x = 3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
27.5
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_007
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-3(3(-1|x - 3| + 1)^2 - 5(-1|x - 3| + 1)))/(2(3(-1|x - 3| + 1)^2 - 5(-1|x - 3| + 1)) + 2) and g(x) = -1((1x + 2)/(-1x - 2))^2 - 4((1x + 2)/(-1x - 2)) + 4 from x = 2.2 to x = 3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
28.4
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_008
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-3|(1x - 2) - 1| + 3))/(1(-3|(1x - 2) - 1| + 3) + 1) and g(x) = 5((-2x - 1)/(-1x + 3))^2 + 4((-2x - 1)/(-1x + 3)) - 2 between the vertical lines x = 1.0 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.4
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_009
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1(2|(-2((-1(1sin(3πx) - 2) - 1)/(2(1sin(3πx) - 2) - 3))^2 + 5((-1(1sin(3πx) - 2) - 1)/(2(1sin(3πx) - 2) - 3)) + 2)| - 2) + 3 and g(x) = 2|(4((3(-1x) + 3)/(1(-1x) - 2))^2 + 2((3(-1x) + 3)/(1(-1x) - 2)) + 1) - 3| - 1 from x = 0.6 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.9
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_010
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3(-3|(3x^2 - 5x - 2) + 2| + 3) - 2, g(x) = -1(2|x + 2| - 1) + 5, x = -0.1, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.5
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_011
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(5(3x - 2)^2 + 3(3x - 2) + 1) + 2)/(-2(5(3x - 2)^2 + 3(3x - 2) + 1) - 3) and g(x) = 1e^(-2(-1|x + 2| + 2)) - 2 between the vertical lines x = -4.5 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
9.7
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_012
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1sin(3π(5(-3|x - 3| - 1) - 3)) and g(x) = 2((-2x + 1)/(-1x - 2))^2 + 4((-2x + 1)/(-1x - 2)) - 2 from x = 0.9 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_013
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|((2(2(1e^(-1x) + 1)^2 - 5(1e^(-1x) + 1) - 1) - 1)/(-1(2(1e^(-1x) + 1)^2 - 5(1e^(-1x) + 1) - 1)))| + 2 and g(x) = 4((3(1x^2 - 1x - 3) + 2)/(2(1x^2 - 1x - 3) + 1)) - 1 between the vertical lines x = -1.1 and x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
23.8
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_014
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-3(-4(-2|(-2x - 4) - 2|)^2 - 2(-2|(-2x - 4) - 2|) + 5))/(-3(-4(-2|(-2x - 4) - 2|)^2 - 2(-2|(-2x - 4) - 2|) + 5) - 3), g(x) = -1((1(-2|x + 3| + 3) + 3)/(2(-2|x + 3| + 3) - 3))^2 + 3((1(-2|x + 3| + 3) + 3)/(2(-2|x + 3| + 3) - 3)) - 1, x = -2.9, and x = -2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.6
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_015
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2sin(3π(5(1x - 1)^2 - 3(1x - 1) + 4) - 1) + 1, g(x) = 2cos(1π(-2x^2 + 3x + 2)) - 1, x = 4.8, and x = 4.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_016
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(3((-3(-2|x - 1| + 1) - 1)/(1(-2|x - 1| + 1) + 3)) - 1)^2 + 1(3((-3(-2|x - 1| + 1) - 1)/(1(-2|x - 1| + 1) + 3)) - 1) + 1 and g(x) = 1|(-1(3sin(3πx + 2) - 1) - 3) - 2| between the vertical lines x = 1.3 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_017
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3|(3((2x - 2)/(3x - 1))^2 - 1((2x - 2)/(3x - 1)) - 1) + 1| - 2 and g(x) = 1(2cos(1πx + 3) - 1) - 2 from x = 2.6 to x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.0
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_018
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1cos(2π((2(-2(1|(2x) - 3|)^2 + 2(1|(2x) - 3|)) + 1)/(2(-2(1|(2x) - 3|)^2 + 2(1|(2x) - 3|)) + 3)) - 2) + 1, g(x) = 5((2(-1|(4x^2 - 4x - 2)| + 2) + 1)/(-3(-1|(4x^2 - 4x - 2)| + 2))) + 3, x = 0.6, and x = 0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_019
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1((-2(-2|x - 3| + 2) - 3)/(1(-2|x - 3| + 2) + 1))^2 + 4((-2(-2|x - 3| + 2) - 3)/(1(-2|x - 3| + 2) + 1)) - 5, g(x) = (3(5x^2 - 2x - 1) + 2)/(2(5x^2 - 2x - 1) - 3), x = -0.5, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
11.2
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_020
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-3|(-1((-2x - 3)/(2x + 1))^2 + 4((-2x - 3)/(2x + 1)) + 2) + 1| - 1) - 5 and g(x) = (-3(-4(-4x^2 + 4) - 4))/(3(-4(-4x^2 + 4) - 4) + 3) between the vertical lines x = -0.7 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.1
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_021
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3cos(3π((1(-2|(4(-4x^2 + 3x + 3) - 4)| - 2) + 2)/(-2(-2|(4(-4x^2 + 3x + 3) - 4)| - 2) - 2)) - 3) + 1 and g(x) = 1|((-2(-5(1x^2 - 1x - 5) + 1) - 3)/(2(-5(1x^2 - 1x - 5) + 1) - 1)) + 2| + 3 from x = 1.1 to x = 1.2000000000000002. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_022
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2(1|(-1x^2 + 5x + 1) + 1|))/(3(1|(-1x^2 + 5x + 1) + 1|) - 2) and g(x) = -5(-3|x + 2|) + 5 from x = -0.5 to x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6.3
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_023
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-3(1|((-1x - 3)/(-3x - 1))| - 2) + 5)^2 - 5(-3(1|((-1x - 3)/(-3x - 1))| - 2) + 5) + 3 and g(x) = -1((2(-1cos(2πx + 1) + 3) + 2)/(-3(-1cos(2πx + 1) + 3) + 1)) between the vertical lines x = -0.0 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.5
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_024
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3(1(2|x + 2| - 2)^2 + 1(2|x + 2| - 2) - 4) - 1, g(x) = (1(5x + 2) - 2)/(2(5x + 2) + 3), x = -3.7, and x = -0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32.2
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_025
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2(4(2sin(3πx) + 3)^2 - 3(2sin(3πx) + 3) - 5) - 2)/(-3(4(2sin(3πx) + 3)^2 - 3(2sin(3πx) + 3) - 5) + 2) and g(x) = 1|((3x + 2)/(-1x + 2)) - 1| + 1 from x = -0.3 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.5
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_026
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2(1((-2(-2cos(3πx) - 3) + 2)/(-2(-2cos(3πx) - 3))) + 2)^2 - 1(1((-2(-2cos(3πx) - 3) + 2)/(-2(-2cos(3πx) - 3))) + 2) + 4 and g(x) = (-1(2|(-3x^2 + 2x + 3)|) - 3)/(-3(2|(-3x^2 + 2x + 3)|) + 4) from x = 1.3 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6.3
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_027
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1|(-3cos(1π(1x^2 - 3x - 4) + 2) + 3) - 1| - 2 and g(x) = 2|((-1x - 3)/(2x + 1)) - 2| from x = -1.4 to x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.6
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_028
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2(-3(-3|x + 1| + 3)^2 + 5(-3|x + 1| + 3) - 2) + 5, g(x) = (-3(-5x + 5) - 1)/(-1(-5x + 5)), x = -1.5, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
11.1
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_029
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3|((-3(-1e^(2(5x + 5))) - 2)/(1(-1e^(2(5x + 5))) - 3)) - 3| + 1, g(x) = -3|(3(-2e^(-1x) + 3)^2 - 3(-2e^(-1x) + 3)) + 1| - 2, x = -0.6, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10.0
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_030
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2e^(2(1(2|x - 3| - 3) + 1)) + 2 and g(x) = 4(-1sin(3πx - 3) - 3) - 3 between the vertical lines x = 1.5 and x = 4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
44.1
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_031
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(3(-2sin(2πx - 2) + 1) + 3) - 2| + 3 and g(x) = 1|(3cos(2πx - 2) + 2) + 2| between the vertical lines x = 0.7 and x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
15.2
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_032
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1|(-2((1x - 3)/(2x + 1))^2 - 2((1x - 3)/(2x + 1)) + 1) + 2| - 2, g(x) = 2e^(-1(-1|x - 3| - 2)) + 3, x = -0.6, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-837.4
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_033
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2sin(1π(-4((2x + 2)/(3x - 1))^2 + 3((2x + 2)/(3x - 1)) + 4) + 2) - 1 and g(x) = -1((-2x - 1)/(-1x + 3)) - 5 from x = 1.5 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.5
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_034
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1|(1((-2x + 1)/(-3x))^2 - 2((-2x + 1)/(-3x)) + 1) + 3| - 1, g(x) = -2e^(-1(1|x - 1| - 2)), x = 0.2, and x = 2.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
9.3
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_035
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1sin(2π(-3(1|x + 1| + 3)^2 + 1(1|x + 1| + 3) - 4)) + 3 and g(x) = 5((2x)/(2x + 3)) - 5 between the vertical lines x = -4.3 and x = -4.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_036
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(4((2(-2x + 4) + 3)/(2(-2x + 4) - 3))^2 - 2) - 3| + 1 and g(x) = (-1(-2(-3x + 4)^2 + 1(-3x + 4) - 2) - 1)/(1(-2(-3x + 4)^2 + 1(-3x + 4) - 2) + 3) between the vertical lines x = 1.5 and x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12.5
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_037
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = 4(2(1|x + 1| - 2) + 3)^2 + 2(2(1|x + 1| - 2) + 3) + 1 and g(x) = 2(-1cos(3πx) - 1) + 2 from x = -1.6 to x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_038
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1sin(2π(1(-2|x + 1|) + 5) - 2), g(x) = -2(3e^(-1x)) + 1, x = 4.2, and x = 4.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_039
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = (1(-2(-3(2sin(1πx + 3) + 3) + 4)^2 + 2) + 2)/(-2(-2(-3(2sin(1πx + 3) + 3) + 4)^2 + 2) - 1) and g(x) = (1(1|(-2x^2 - 3x - 1) + 2| - 2) + 3)/(1(1|(-2x^2 - 3x - 1) + 2| - 2) - 3) from x = 0.7 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_040
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-1cos(3π(-4(-2|x + 2| + 3) + 2) - 2) + 1) + 3)/(-1(-1cos(3π(-4(-2|x + 2| + 3) + 2) - 2) + 1) - 2) and g(x) = -1|(2((1x - 3)/(-1x + 2)) + 3) + 2| + 2 between the vertical lines x = 4.8 and x = 4.8999999999999995. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_041
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1|((-2(-1cos(3π(-1x - 5)) + 3) - 3)/(1(-1cos(3π(-1x - 5)) + 3))) - 2| + 2, g(x) = -1(-5(1|x + 2|) + 3)^2 + 2(-5(1|x + 2|) + 3) - 4, x = -1.7, and x = -1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_042
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(5(-4(1|x + 2| - 2) - 4)^2 + 1(-4(1|x + 2| - 2) - 4) - 3) - 2)/(2(5(-4(1|x + 2| - 2) - 4)^2 + 1(-4(1|x + 2| - 2) - 4) - 3) - 1) and g(x) = (2(5(-3|x + 2| + 2) + 3) + 2)/(-3(5(-3|x + 2| + 2) + 3) - 1) between the vertical lines x = -1.3 and x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.4
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_043
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(4((-3(3e^(-2x) - 2))/(-2(3e^(-2x) - 2) + 3)) + 2) - 3| + 3 and g(x) = (3(-1(-2|x + 2| + 2)^2 + 5(-2|x + 2| + 2) - 5) + 1)/(-2(-1(-2|x + 2| + 2)^2 + 5(-2|x + 2| + 2) - 5) + 1) between the vertical lines x = -2.2 and x = -1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
22.1
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_044
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3(2|((3(2x + 1) + 3)/(-2(2x + 1) - 3)) + 2| - 2)^2 + 5(2|((3(2x + 1) + 3)/(-2(2x + 1) - 3)) + 2| - 2) - 1 and g(x) = 2|(-5(5x^2 + 4x) + 3) - 2| - 3 from x = -0.9 to x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.3
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_045
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3|(3cos(1π(1(-2x^2 - 3x) + 2) - 2) + 2) - 3|, g(x) = -1|(3e^(-2((-2x - 1)/(2x))) - 1) + 3| + 3, x = -0.1, and x = 0.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_046
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(3π(5((-2x - 1)/(1x - 2)) + 4)) - 3 and g(x) = -3|(-1sin(2πx - 3)) - 1| - 2 between the vertical lines x = 1.4 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_047
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(2sin(2π((1x - 3)/(1x + 1)) - 3) - 2) - 2| - 1 and g(x) = (-1(3x + 2) - 2)/(-3(3x + 2) - 2) between the vertical lines x = -0.9 and x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.5
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_048
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1(1(3e^(-1x) - 1))^2 + 2(1(3e^(-1x) - 1)) - 1 and g(x) = 2cos(3π(-5x + 3) - 2) + 1 from x = 0.6 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
algebra_func_area
|
test_out
|
algebra_func_area_test_out_049
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3(1((1(-2|x - 3| + 1) + 1)/(1(-2|x - 3| + 1) - 3))^2 - 5((1(-2|x - 3| + 1) + 1)/(1(-2|x - 3| + 1) - 3)) - 5) + 3, g(x) = 3|(-2e^(-1(-2x^2 + 5x + 1)) + 3) + 1| - 3, x = 2.8, and x = 2.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
algebra_func_area
|
test_out
|
algebra_func_derivative_sign_test_in_000
|
algebra_func_derivative_sign
|
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3cos(3π(-4(3((-2x)/(-2x - 2))^2 - 3((-2x)/(-2x - 2)) - 3) + 4) - 1) + 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
18
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_001
|
algebra_func_derivative_sign
|
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2(1(3cos(1π(3|x| + 1) + 1) + 3) + 4)^2 - 1(1(3cos(1π(3|x| + 1) + 1) + 3) + 4) + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
31
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_002
|
algebra_func_derivative_sign
|
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2|(-1(4((3x - 2)/(1x + 1)))^2 - 2(4((3x - 2)/(1x + 1))) + 2) + 3| - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_003
|
algebra_func_derivative_sign
|
[
{
"content": "For the function f(x) = (-3(3(5(3|x + 3|)^2 - 4(3|x + 3|) - 4) - 4) + 1)/(-3(3(5(3|x + 3|)^2 - 4(3|x + 3|) - 4) - 4) + 2), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_004
|
algebra_func_derivative_sign
|
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2sin(1π(1x^2 - 5x + 5) - 1) + 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
55
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_005
|
algebra_func_derivative_sign
|
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1sin(1π(-4(1x^2 + 5x - 1) + 3)) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
42
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_006
|
algebra_func_derivative_sign
|
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2((1x - 2)/(3x + 2))^2 + 2((1x - 2)/(3x + 2)) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_007
|
algebra_func_derivative_sign
|
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|(-2cos(1πx - 1) + 2) + 1| - 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
11
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_008
|
algebra_func_derivative_sign
|
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -4(-1sin(2π((1x - 3)/(-3x - 1)) - 1) - 3)^2 + 3(-1sin(2π((1x - 3)/(-3x - 1)) - 1) - 3) - 5 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_009
|
algebra_func_derivative_sign
|
[
{
"content": "For the function f(x) = -2|(1((-3(4x - 5) - 3)/(1(4x - 5) - 2))^2 - 4((-3(4x - 5) - 3)/(1(4x - 5) - 2)) - 1) - 2| - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_010
|
algebra_func_derivative_sign
|
[
{
"content": "For the function f(x) = -3((2(2|x - 1| - 1) + 3)/(1(2|x - 1| - 1) + 3))^2 + 5((2(2|x - 1| - 1) + 3)/(1(2|x - 1| - 1) + 3)) + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_011
|
algebra_func_derivative_sign
|
[
{
"content": "For the function f(x) = -2(-2sin(1π(-2|x + 3| - 2) + 3) + 3)^2 - 1(-2sin(1π(-2|x + 3| - 2) + 3) + 3) - 4, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
21
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_012
|
algebra_func_derivative_sign
|
[
{
"content": "For the function f(x) = -2sin(2π(-3|x| - 3) + 3) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
61
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_013
|
algebra_func_derivative_sign
|
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(1((2x - 2)/(3x + 2))^2) + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_014
|
algebra_func_derivative_sign
|
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|((1x + 2)/(-1x - 1)) + 3| is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_015
|
algebra_func_derivative_sign
|
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1sin(2π((3x - 2)/(3x + 3)) - 2) - 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_016
|
algebra_func_derivative_sign
|
[
{
"content": "For the function f(x) = -1|(1sin(2π(2x^2 - 2x) - 1))| + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
43
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_017
|
algebra_func_derivative_sign
|
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3(3((2x + 2)/(3x - 2))^2 - 2((2x + 2)/(3x - 2))) - 5 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_018
|
algebra_func_derivative_sign
|
[
{
"content": "For the function f(x) = 1|(1(3e^(-1x) - 2)^2 - 5(3e^(-1x) - 2) - 4) + 3| + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_019
|
algebra_func_derivative_sign
|
[
{
"content": "For the function f(x) = (-1(-2|(1sin(1πx + 2) + 1) + 3| - 3) - 3)/(-3(-2|(1sin(1πx + 2) + 1) + 3| - 3) + 2), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_020
|
algebra_func_derivative_sign
|
[
{
"content": "For the function f(x) = 5(3cos(2π(5x - 1) + 1))^2 + 3(3cos(2π(5x - 1) + 1)) - 5, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_021
|
algebra_func_derivative_sign
|
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2cos(3π(-4(-3|x - 1| + 1)^2 + 5(-3|x - 1| + 1) + 3)) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
9
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_022
|
algebra_func_derivative_sign
|
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 4(-2cos(2πx + 1) - 1) + 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
21
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_023
|
algebra_func_derivative_sign
|
[
{
"content": "For the function f(x) = (2(5(-2cos(3πx + 3) + 3)^2 + 4(-2cos(3πx + 3) + 3) + 4) - 3)/(1(5(-2cos(3πx + 3) + 3)^2 + 4(-2cos(3πx + 3) + 3) + 4) - 3), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
31
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_024
|
algebra_func_derivative_sign
|
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3|((2(1(3cos(3πx - 1) + 2) - 5) + 3)/(3(1(3cos(3πx - 1) + 2) - 5) - 2)) + 2| positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
31
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_025
|
algebra_func_derivative_sign
|
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (2(-2cos(1πx + 3) - 3) - 1)/(2(-2cos(1πx + 3) - 3) - 3) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_026
|
algebra_func_derivative_sign
|
[
{
"content": "For the function f(x) = 1cos(1π(-1x^2 - 3x + 4) + 1) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
55
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_027
|
algebra_func_derivative_sign
|
[
{
"content": "For the function f(x) = (-1(-3(-1(3|x - 3| - 1) + 3)^2 - 1(-1(3|x - 3| - 1) + 3) + 2) - 2)/(-1(-3(-1(3|x - 3| - 1) + 3)^2 - 1(-1(3|x - 3| - 1) + 3) + 2) + 2), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_028
|
algebra_func_derivative_sign
|
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2sin(3π(-4(-3((2x + 3)/(1x + 1))^2 + 5((2x + 3)/(1x + 1)) + 5) + 1) + 3) - 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
33
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_029
|
algebra_func_derivative_sign
|
[
{
"content": "For the function f(x) = -1sin(2π(-2|x - 1| - 3) + 2) + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
40
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_030
|
algebra_func_derivative_sign
|
[
{
"content": "For the function f(x) = 5(-1cos(2πx - 3) + 3) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
21
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_031
|
algebra_func_derivative_sign
|
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2cos(2π(5(-1x - 3)^2 + 2(-1x - 3)) - 2) + 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
44
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_032
|
algebra_func_derivative_sign
|
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2sin(2π(4x + 3) - 3) - 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
80
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_033
|
algebra_func_derivative_sign
|
[
{
"content": "For the function f(x) = (3(2(3sin(2πx - 1) + 1) + 2) + 1)/(1(2(3sin(2πx - 1) + 1) + 2) - 3), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
21
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_034
|
algebra_func_derivative_sign
|
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (2(-3(4(2|x - 2|) - 5)^2 + 4(4(2|x - 2|) - 5) + 4) + 2)/(-2(-3(4(2|x - 2|) - 5)^2 + 4(4(2|x - 2|) - 5) + 4) - 3) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_035
|
algebra_func_derivative_sign
|
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2(2|(-1cos(3π(3x^2 + 3x - 1) - 1) + 1)|) + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
42
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_036
|
algebra_func_derivative_sign
|
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(-3|(1x - 5) + 1| + 1)^2 - 5 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_037
|
algebra_func_derivative_sign
|
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-1(3|(-1sin(2π(1x^2 - 5x) + 2) + 1)| + 1) - 2)/(-1(3|(-1sin(2π(1x^2 - 5x) + 2) + 1)| + 1) + 3) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
44
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_038
|
algebra_func_derivative_sign
|
[
{
"content": "For the function f(x) = 5(-2|((-1(-1x + 3) - 1)/(3(-1x + 3) - 1)) - 1| - 3)^2 - 4(-2|((-1(-1x + 3) - 1)/(3(-1x + 3) - 1)) - 1| - 3) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_039
|
algebra_func_derivative_sign
|
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -4(-2cos(3π(-2x^2 + 3x - 3) + 2) + 3) + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
27
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_040
|
algebra_func_derivative_sign
|
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(-1cos(2π(4x + 3) + 1) - 3)^2 + 2(-1cos(2π(4x + 3) + 1) - 3) + 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
81
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_041
|
algebra_func_derivative_sign
|
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(2sin(1πx + 3) - 3) - 5 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_042
|
algebra_func_derivative_sign
|
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1|(4(-1e^(1(-4x^2 - 3x + 2))) - 3) + 3| - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_043
|
algebra_func_derivative_sign
|
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|(-2sin(1π(-1(-2x^2 + 4x + 5) + 4) - 3) + 3) + 2| is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
47
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_044
|
algebra_func_derivative_sign
|
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2sin(3π(5(1|(3x + 3) + 3| + 3)^2 - 3(1|(3x + 3) + 3| + 3) + 5) - 1) + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
9
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_045
|
algebra_func_derivative_sign
|
[
{
"content": "For the function f(x) = -2((2(-1|x + 3| + 1) - 3)/(1(-1|x + 3| + 1) + 2))^2 + 4((2(-1|x + 3| + 1) - 3)/(1(-1|x + 3| + 1) + 2)) - 4, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_046
|
algebra_func_derivative_sign
|
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(2cos(2π(-5((2x - 2)/(-2x - 1))^2 - 3((2x - 2)/(-2x - 1)) + 1) + 1) + 3) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
19
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_047
|
algebra_func_derivative_sign
|
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2|(-5(1((1x + 2)/(2x - 3))^2 - 5((1x + 2)/(2x - 3)) + 2) - 1) - 1| - 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_048
|
algebra_func_derivative_sign
|
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3((3(-3|(-5x^2 - 5x + 2)| + 2) - 3)/(-3(-3|(-5x^2 - 5x + 2)| + 2) + 1)) + 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
math
|
algebra_func_derivative_sign
|
test_in
|
algebra_func_derivative_sign_test_in_049
|
algebra_func_derivative_sign
|
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 4(-1cos(2πx - 2) - 2) - 5 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
21
|
math
|
algebra_func_derivative_sign
|
test_in
|
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