Dataset Viewer
id
stringlengths 26
62
| setting_key
stringclasses 41
values | messages
listlengths 1
1
| ground_truth
stringlengths 1
9
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stringclasses 1
value | omega_config
stringclasses 41
values | omega_split
stringclasses 2
values |
|---|---|---|---|---|---|---|
algebra_func_area_test_in_000
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2(-3x + 4)^2 + 1(-3x + 4) + 3, g(x) = 3x - 1, x = 1.3, and x = 1.7. 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_in
|
algebra_func_area_test_in_001
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1|((2(-2sin(1πx + 2) - 3) - 1)/(-1(-2sin(1πx + 2) - 3) + 3)) + 2| - 3, g(x) = -2e^(-1(-5x)) - 2, x = -3.5, and x = -2.8. 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_in
|
algebra_func_area_test_in_002
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1(-3(3x + 5)^2 + 1(3x + 5) + 5) + 3)/(2(-3(3x + 5)^2 + 1(3x + 5) + 5) - 1), g(x) = -3|(1x^2 + 4x + 1) + 3| + 3, x = -1.2, and x = -0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.9
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_003
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1sin(2π(-1|((1x + 2)/(3x - 1))|) + 2) + 1 and g(x) = (-1(5x - 3) - 3)/(-2(5x - 3) + 1) from x = -0.2 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.8
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_004
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|((3x + 2)/(-2x - 1)) + 2| - 1 and g(x) = 4x^2 + 2x - 4 between the vertical lines x = -0.6 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10.8
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_005
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2(5(-1cos(2π(-1|x + 1| + 2) + 1) - 1)^2 + 2(-1cos(2π(-1|x + 1| + 2) + 1) - 1) - 1) - 2 and g(x) = (-1(2|(-1cos(3πx - 1) + 2) - 2| + 1) + 1)/(-1(2|(-1cos(3πx - 1) + 2) - 2| + 1) - 1) from x = -2.7 to x = -1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
11.4
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_006
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = (2(-2(4(-3|x|) + 4)^2 + 1(4(-3|x|) + 4)) - 1)/(-3(-2(4(-3|x|) + 4)^2 + 1(4(-3|x|) + 4))) and g(x) = 1cos(3π((-3(5x - 1) + 1)/(3(5x - 1) + 1)) + 3) + 2 from x = 0.3 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.5
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_007
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(2|(-1((2x - 1)/(1x + 1))^2 + 4((2x - 1)/(1x + 1)) + 5) + 3| + 2) and g(x) = -1|(2sin(2π((2x - 3)/(2x + 1)) + 2) + 1) + 3| - 3 between the vertical lines x = -0.1 and x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_008
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2cos(2π(-3((-3x + 3)/(3x - 2))^2 + 4((-3x + 3)/(3x - 2)) - 1) + 3) - 1 and g(x) = (-3(4x + 4) - 2)/(-2(4x + 4) + 1) from x = -1.6 to x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.0
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_009
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = -5((1x + 2)/(1x + 2))^2 - 3((1x + 2)/(1x + 2)) - 4 and g(x) = -3x^2 - 5x - 4 from x = -2.7 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
24.7
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_010
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = (2(1(3|(1x + 3) + 2|)^2 + 5) + 2)/(2(1(3|(1x + 3) + 2|)^2 + 5) + 3) and g(x) = (3(-3|(1x^2 + 4x) + 2| + 1) + 3)/(2(-3|(1x^2 + 4x) + 2| + 1) - 3) from x = -4.0 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.3
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_011
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = (3(-2(1(2sin(2πx - 2) + 1) + 3)^2 - 1(1(2sin(2πx - 2) + 1) + 3) - 5) - 1)/(2(-2(1(2sin(2πx - 2) + 1) + 3)^2 - 1(1(2sin(2πx - 2) + 1) + 3) - 5) + 3) and g(x) = -4(4(2|x - 2| - 1) - 1)^2 - 5(4(2|x - 2| - 1) - 1) + 2 from x = 2.5 to x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_012
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3((3(2|x - 3| - 2) - 3)/(3(2|x - 3| - 2) + 2))^2 + 4((3(2|x - 3| - 2) - 3)/(3(2|x - 3| - 2) + 2)) and g(x) = -3|(-2e^(1x) - 3) + 1| + 1 between the vertical lines x = 3.6 and x = 3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-88.2
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_013
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2|(5x + 2) - 2| + 3 and g(x) = 2|x + 3| + 1 from x = -0.3 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.7
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_014
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1((-1(1|(2x - 2) + 2| - 2) - 2)/(-2(1|(2x - 2) + 2| - 2) - 3))^2, g(x) = (-3(1(-3cos(1πx + 1) + 1) - 1) - 1)/(2(1(-3cos(1πx + 1) + 1) - 1) + 3), x = 3.2, and x = 4.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
11.6
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_015
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = (3(2|(-2cos(2πx) + 1) - 2|) + 3)/(3(2|(-2cos(2πx) + 1) - 2|) + 1) and g(x) = -3(2cos(1πx + 2) + 1)^2 + 5(2cos(1πx + 2) + 1) + 5 from x = 3.7 to x = 4.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.9
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_016
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(3cos(3π(-1x^2 - 4x - 1) + 2) - 1) - 3| and g(x) = -1((-1x - 3)/(1x + 1))^2 - 4((-1x - 3)/(1x + 1)) + 1 between the vertical lines x = -1.6 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-27.4
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_017
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1|(-3cos(1π(4(-4x^2 - 1x + 5) - 5) + 3) - 1)| + 1, g(x) = 2|(-3(5x - 4)^2 - 1(5x - 4) - 3) + 2|, x = 0.7, and x = 0.7999999999999999. 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_in
|
algebra_func_area_test_in_018
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1|(2cos(2πx + 3) + 1) - 1| - 3 and g(x) = 1x^2 + 5x from x = -4.6 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12.9
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_019
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1|(4((2x)/(-3x + 4)) - 3)| - 3, g(x) = -3|(-2x^2 + 2x + 5) - 2|, x = -1.2, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.1
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_020
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(3π(2|x - 2| - 2) - 2) + 3 and g(x) = 4x^2 - 5x between the vertical lines x = 1.7 and x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_021
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3sin(3π((-1x - 1)/(-1x - 3)) + 2) - 2 and g(x) = 1x^2 + 1x - 4 from x = -2.5 to x = -2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_022
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = 4(-1sin(2π((1x + 2)/(-1x + 2)) - 3)) - 3, g(x) = -3e^(1(-4x^2 + 5x - 2)) + 1, x = 1.8, and x = 1.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.4
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_023
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-1(-3|(4x^2 + 2x - 3) - 2| + 3) + 3)/(-2(-3|(4x^2 + 2x - 3) - 2| + 3) - 1) and g(x) = 2e^(1(-4x - 5)) - 2 from x = 0.8 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.3
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_024
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-1|(1x + 5) + 3| - 2) + 3)/(-3(-1|(1x + 5) + 3| - 2) + 1) and g(x) = 4(-2cos(1πx) + 1) - 4 between the vertical lines x = 1.5 and x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.9
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_025
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-5(1|x + 2| + 3) + 2) + 2)/(-2(-5(1|x + 2| + 3) + 2) - 1) and g(x) = 2|(-5x^2 - 1x + 4) - 2| - 2 between the vertical lines x = 0.5 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_026
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(3|(-5(-2x^2 + 3) + 2) - 2| - 2) + 2)/(-1(3|(-5(-2x^2 + 3) + 2) - 2| - 2) - 1) and g(x) = -1|(-2sin(1π((2x + 1)/(-1x + 2)) + 2) + 2) - 2| between the vertical lines x = 2.0 and x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_027
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1|(-1((-3(1x^2 - 3x + 5) + 1)/(1(1x^2 - 3x + 5) + 2)) - 4) - 2| + 3 and g(x) = 3|(-1(2sin(3πx + 1) - 1) + 2)| + 3 from x = -1.9 to x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.7
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_028
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2cos(2π(4(1x^2 + 3x - 2) - 1) - 3) - 3 and g(x) = 1cos(1π(-2x^2 - 5x - 2) - 3) - 2 from x = 2.6 to x = 2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_029
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = -5(-3sin(3πx - 1) - 1) + 3, g(x) = -2|x| - 1, x = -0.8, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.6
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_030
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-2(3|x - 2| - 3) + 2)/(-2(3|x - 2| - 3)), g(x) = -1|x + 2| + 1, x = -2.1, and x = -1.9. 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_in
|
algebra_func_area_test_in_031
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(-5(-1sin(3πx) + 2) - 2))/(2(-5(-1sin(3πx) + 2) - 2) + 3) and g(x) = -1(4x^2 - 2x + 2) + 2 between the vertical lines x = -0.5 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.9
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_032
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2|(1((-2(-4x - 1) + 1)/(-3(-4x - 1) + 4))^2 + 4) - 1| - 2 and g(x) = -1(-2|(1x + 1) + 1| + 1)^2 + 4(-2|(1x + 1) + 1| + 1) + 3 from x = -3.5 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
27.5
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_033
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2(3cos(2πx + 3) - 2)^2 - 4(3cos(2πx + 3) - 2) + 3 and g(x) = 1|x + 1| + 1 from x = -2.4 to x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
26.2
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_034
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1e^(2(4x^2 + 4x - 3)) + 1 and g(x) = -2|x + 1| between the vertical lines x = -1.6 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.6
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_035
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2sin(1π(-1(-5(3|x + 1| - 3)^2 + 5(3|x + 1| - 3) + 3) + 4) + 1) + 3, g(x) = (-3(3(1x + 5)^2 - 3(1x + 5) - 5) - 2)/(1(3(1x + 5)^2 - 3(1x + 5) - 5)), x = -3.2, and x = -3.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.9
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_036
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1cos(3π(1(-4((-1x + 2)/(-3x - 2)) + 5)^2 - 3(-4((-1x + 2)/(-3x - 2)) + 5) + 2) - 2) + 2 and g(x) = (-1(1|(-2e^(2x) - 1) + 3| - 1) + 1)/(-1(1|(-2e^(2x) - 1) + 3| - 1)) from x = -0.0 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_037
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(2e^(-1x) - 2) - 2| + 3 and g(x) = 2|x + 2| - 2 between the vertical lines x = -1.0 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.7
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_038
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-2x^2 - 5x + 2)| - 3 and g(x) = -1x + 4 between the vertical lines x = -4.1 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
24.9
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_039
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2e^(-2(2(1x^2 + 2x + 2) - 3)) + 2 and g(x) = -3sin(3π((-1x + 2)/(-3x + 2)) - 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"
}
] |
0.2
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_040
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1(3x^2 + 5x - 4) - 3, g(x) = (-1x)/(-2x - 2), x = -1.2, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
25.6
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_041
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2|(3cos(3πx - 3) + 3)| + 3 and g(x) = (2x - 3)/(1x + 2) from x = -3.5 to x = -3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.8
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_042
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2(3cos(1πx + 2) + 2)^2 + 5(3cos(1πx + 2) + 2) - 3 and g(x) = 4x^2 + 1x - 4 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"
}
] |
0.1
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_043
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = (3(-2|(-3x^2 - 2x - 3) - 2| - 3) - 1)/(-2(-2|(-3x^2 - 2x - 3) - 2| - 3) - 2) and g(x) = -3(-3x + 3)^2 - 3(-3x + 3) - 2 from x = 1.0 to x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_044
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = (3(-3|(-2cos(1πx + 2) + 2) - 1| - 2) + 3)/(3(-3|(-2cos(1πx + 2) + 2) - 1| - 2) - 1) and g(x) = (1(1|x + 2| + 1))/(2(1|x + 2| + 1) + 1) from x = -5.0 to x = -4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_045
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-4x - 2)^2 + 3(-4x - 2) + 2 and g(x) = (-2x - 1)/(-3x + 1) between the vertical lines x = -0.4 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6.6
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_046
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(-3sin(3πx + 1) + 3) + 1| + 3 and g(x) = 3|x - 2| + 3 between the vertical lines x = -3.7 and x = -3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.6
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_047
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(1(-2|(-5x - 2) - 2| + 2)^2 + 4(-2|(-5x - 2) - 2| + 2) + 3) + 2)/(3(1(-2|(-5x - 2) - 2| + 2)^2 + 4(-2|(-5x - 2) - 2| + 2) + 3) - 2) and g(x) = -4(2|((-2x - 2)/(3x - 2)) + 3| - 3) + 3 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"
}
] |
1.6
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_048
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(3sin(3πx + 1) + 3)^2 - 3(3sin(3πx + 1) + 3) - 3 and g(x) = -1x^2 - 3x - 3 between the vertical lines x = 0.3 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_049
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2|(3x + 3) + 2| + 2, g(x) = -2|x - 2| - 2, x = -4.5, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
24.1
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_050
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1|(-2(5x^2 + 2x) + 1)| + 1 and g(x) = 3(1sin(2πx) - 3) - 2 from x = -1.4 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
20.1
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_051
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3|(-3(-1x^2 - 4x - 3) + 3) - 2| + 3 and g(x) = (-2(5x + 3) - 2)/(1(5x + 3) - 2) from x = -3.1 to x = -2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.5
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_052
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-3(2(1e^(2x) - 1)) + 1)/(1(2(1e^(2x) - 1)) - 2), g(x) = -4(-1x^2 + 4x), x = 0.0, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
20.3
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_053
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-1(-1sin(3πx - 1) + 3) - 3)/(1(-1sin(3πx - 1) + 3)) and g(x) = 3|x| - 2 from x = -0.1 to x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_054
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1(3cos(3πx + 2) + 2) - 5, g(x) = 3x + 3, x = -2.4, and x = -2.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.9
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_055
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = -4(-3|(3(1e^(-2x) - 3)^2 - 5(1e^(-2x) - 3) - 4) + 1| + 1) - 2 and g(x) = (-1(4(3sin(3πx + 1) - 1) + 3) - 1)/(-2(4(3sin(3πx + 1) - 1) + 3) + 3) from x = -0.8 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12.1
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_056
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3cos(1π(3|x - 3| - 1) - 1) - 2 and g(x) = 4x + 2 between the vertical lines x = -1.5 and x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_057
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(4x)^2 + 3(4x) and g(x) = 2x between the vertical lines x = 0.0 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_058
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3|(-2sin(2πx - 2) + 3) + 2| + 1 and g(x) = -4x - 3 from x = -3.5 to x = -3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_059
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(1|(-1(-3e^(1x) + 1)^2 + 3) - 2| - 3) - 2 and g(x) = -3sin(1π(-1|(-2x + 3) + 1| + 3) + 2) between the vertical lines x = -1.3 and x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.9
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_060
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = (1(-3cos(1πx + 1) - 2) + 3)/(1(-3cos(1πx + 1) - 2)), g(x) = (2x - 1)/(3x + 3), x = 0.1, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
13.0
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_061
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-1(-3|x - 1| + 2) - 2)^2 + 3 and g(x) = (1(2x^2 + 2) + 2)/(-3(2x^2 + 2) - 3) between the vertical lines x = 2.1 and x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.2
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_062
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(-3|((1(4x^2 - 1x - 5) + 2)/(1(4x^2 - 1x - 5) - 2)) - 1|) + 1 and g(x) = (-2(-4(2|x + 1| + 3) + 4) - 2)/(2(-4(2|x + 1| + 3) + 4)) between the vertical lines x = -2.1 and x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
35.8
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_063
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(3π((2(-3x + 4) - 3)/(3(-3x + 4) - 2)) + 2) + 3 and g(x) = -3cos(2π(-1x + 5) - 2) + 1 between the vertical lines x = 1.1 and 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_in
|
algebra_func_area_test_in_064
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2|(-2sin(2π((-2x + 1)/(-1x - 1))) - 1) + 1| - 1, g(x) = -1((-2x + 1)/(-2x + 3)) - 4, x = -1.4, and x = -1.2999999999999998. 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_in
|
algebra_func_area_test_in_065
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2|(-1(5((3x + 1)/(3x + 2))^2 - 4((3x + 1)/(3x + 2)) + 5) + 5) - 1| + 3 and g(x) = -5(-1sin(1π((-2x - 1)/(1x + 1)) + 2) + 1)^2 - 5(-1sin(1π((-2x - 1)/(1x + 1)) + 2) + 1) - 5 from x = -1.0 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.4
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_066
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(3cos(1πx) + 3) + 1| + 1 and g(x) = 3x - 1 between the vertical lines x = 2.6 and x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.0
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_067
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2(5x^2 + 3x - 4) - 5 and g(x) = -4x^2 - 3x - 2 from x = -1.3 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
15.7
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_068
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1(2|(-5((2x + 3)/(2x - 1))^2 - 4((2x + 3)/(2x - 1)) + 5) + 2| - 3) - 3 and g(x) = (-1(-2|(-5x^2 + 1) + 1| + 3))/(1(-2|(-5x^2 + 1) + 1| + 3)) from x = -0.3 to x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_069
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3|(3x - 4) + 2| - 3 and g(x) = -5x^2 + 3x + 2 from x = -2.2 to x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
34.1
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_070
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2e^(-1(2((-3(-2|x + 2|) - 3)/(1(-2|x + 2|) - 2)) + 2)) + 3, g(x) = (3(-3sin(1π(2x - 5) - 1) - 1) - 3)/(3(-3sin(1π(2x - 5) - 1) - 1) - 2), x = -1.8, and x = -1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.2
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_071
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(3|x + 3| + 3) - 1 and g(x) = 2|x| + 2 between the vertical lines x = -3.8 and x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.7
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_072
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3|(-4(1((1x + 3)/(-2x + 3)) - 3)^2 - 4(1((1x + 3)/(-2x + 3)) - 3) + 3) + 2| - 1 and g(x) = (3(3|(-2sin(2πx + 2) + 3) - 3| + 3) - 3)/(2(3|(-2sin(2πx + 2) + 3) - 3| + 3) - 1) from x = 0.2 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_073
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2(4(2|((3x)/(2x + 1)) - 3|) - 5)^2 - 1(4(2|((3x)/(2x + 1)) - 3|) - 5) + 4, g(x) = (-1(5(1e^(1x) - 3) - 3) - 2)/(1(5(1e^(1x) - 3) - 3) - 2), x = -0.9, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.4
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_074
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(3|(-2e^(1(3x - 1)) - 2) - 3| + 1) - 1)/(3(3|(-2e^(1(3x - 1)) - 2) - 3| + 1) + 2) and g(x) = 2(-3e^(2(-3|x + 1| - 1)) - 1)^2 - 4 between the vertical lines x = -1.0 and x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_075
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3|(2x + 2) + 2| - 2 and g(x) = 1|x - 3| from x = -3.4 to x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8.4
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_076
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1|(-5((2(4x + 1) + 1)/(-2(4x + 1) + 1))^2 - 2((2(4x + 1) + 1)/(-2(4x + 1) + 1)) + 1) + 1| - 1, g(x) = -2(-2cos(1π(-2|x - 2| + 3) - 1) - 1) - 4, x = 4.1, and x = 4.6. 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_in
|
algebra_func_area_test_in_077
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3|(-5((3(-4x + 5) + 3)/(-1(-4x + 5) - 3))^2 - 4) - 1| + 2 and g(x) = 4(-2sin(2π(-2|x| + 2) + 2) + 2)^2 + 2(-2sin(2π(-2|x| + 2) + 2) + 2) - 1 from x = 1.2 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.5
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_078
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1(3(2|x + 1| + 2)^2 + 5(2|x + 1| + 2) - 2) + 2)/(1(3(2|x + 1| + 2)^2 + 5(2|x + 1| + 2) - 2) + 3), g(x) = 4(3x - 3)^2 - 1(3x - 3) - 3, x = 0.8, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.7
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_079
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-3(3|x| - 3)^2 + 1(3|x| - 3) + 1) + 3)/(2(-3(3|x| - 3)^2 + 1(3|x| - 3) + 1) + 1) and g(x) = (3(1x^2 + 4x - 2) + 3)/(-1(1x^2 + 4x - 2)) between the vertical lines x = -4.3 and x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10.8
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_080
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1((-2(5x^2 - 5x - 2) + 2)/(2(5x^2 - 5x - 2) - 1)) - 1, g(x) = 1sin(2π(2|x - 1|) - 3) - 2, x = -0.4, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.0
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_081
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-3e^(-1(-5(-1|x| - 2) - 2)) + 1)^2 - 1(-3e^(-1(-5(-1|x| - 2) - 2)) + 1) - 2 and g(x) = -2|(-1cos(1π(-2x - 2) + 1) + 2) + 1| 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"
}
] |
2.0
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_082
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-2sin(1π((2(-5x^2 + 2x) - 2)/(2(-5x^2 + 2x) - 1)) - 1) - 1) - 2| - 2 and g(x) = 2e^(1(-5(3x^2 + 2x - 1) - 3)) - 2 between the vertical lines x = -0.8 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32.6
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_083
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1e^(-2(-3|x - 2| - 1)) + 1 and g(x) = -3x - 1 from x = 2.0 to x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_084
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3sin(3π(1|((-3(-1x - 5) - 1)/(1(-1x - 5) + 2)) - 2| + 3) + 2) + 2 and g(x) = (2(2|(-5x^2 + 3x - 3) - 1| - 2) - 2)/(-3(2|(-5x^2 + 3x - 3) - 1| - 2) + 2) from x = -4.2 to x = -4.1000000000000005. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.4
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_085
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1|(3e^(1((-1x)/(-2x - 2))) - 1) + 1| - 3 and g(x) = 2(-5x^2 + 2x + 2) + 1 from x = -0.6 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.2
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_086
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(1(5((1x - 1)/(-1x + 2))^2 + 2((1x - 1)/(-1x + 2)) - 1) + 3) - 3| + 1 and g(x) = 2|(-2((3x + 1)/(-1x + 2))^2 + 3((3x + 1)/(-1x + 2)) + 1) - 2| - 1 between the vertical lines x = -0.4 and x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.7
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_087
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-2cos(3π(2|x - 2|) - 2) - 1) - 4 and g(x) = 4(-1e^(1x))^2 - 5(-1e^(1x)) - 3 between the vertical lines x = -1.7 and x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.8
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_088
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1(-1(4x + 3)^2 - 2(4x + 3) + 2))/(-2(-1(4x + 3)^2 - 2(4x + 3) + 2)), g(x) = -1((2x)/(-1x + 2))^2 + 4((2x)/(-1x + 2)) + 2, x = -0.4, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.5
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_089
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3sin(3π(-1x - 2) + 1) + 2 and g(x) = 4x - 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_in
|
algebra_func_area_test_in_090
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3cos(1π(5((1x)/(2x + 1))^2 - 5((1x)/(2x + 1)) - 2) - 3) and g(x) = -3|(-3x + 3) + 3| - 1 between the vertical lines x = 1.8 and x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.3
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_091
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1(1(1sin(3πx + 1) + 2)^2 - 2(1sin(3πx + 1) + 2) - 2) + 2, g(x) = (1(1x + 2) + 2)/(2(1x + 2) + 3), x = -1.1, and x = -0.7. 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_in
|
algebra_func_area_test_in_092
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1|((1(1cos(3π(2x^2 - 1x + 3) + 3) + 3) + 2)/(2(1cos(3π(2x^2 - 1x + 3) + 3) + 3) + 1)) - 2| - 3, g(x) = -3cos(1π(3|(-2x) - 3| - 3) - 1) - 3, x = 4.7, and x = 4.8. 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_in
|
algebra_func_area_test_in_093
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1((3(-1|(-2x - 5) + 1|) - 2)/(3(-1|(-2x - 5) + 1|) - 2))^2 + 3((3(-1|(-2x - 5) + 1|) - 2)/(3(-1|(-2x - 5) + 1|) - 2)) + 1, g(x) = (-3(1(1x)^2) + 1)/(1(1(1x)^2)), x = -0.4, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-9.8
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_094
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3|(2cos(3π((3(-4x^2 + 4x - 3) + 2)/(3(-4x^2 + 4x - 3)))) + 1) + 1| - 2, g(x) = -3(-2|(2x^2 - 4x) - 2| + 2) + 1, x = 2.3, and x = 2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.3
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_095
|
algebra_func_area
|
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3sin(3π(1|x + 1| - 1) + 2) - 2 and g(x) = 2x^2 + 4x + 2 from x = -1.0 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_096
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-2e^(-2x) + 3) - 3)/(2(-2e^(-2x) + 3) + 2) and g(x) = -3|x + 3| + 1 between the vertical lines x = -2.3 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
7.4
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_097
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-3|(3(1cos(1πx + 1) + 3) + 1) + 2| - 1))/(-2(-3|(3(1cos(1πx + 1) + 3) + 1) + 2| - 1) - 2) and g(x) = -3(-3|(-2x + 3)| + 2)^2 + 5(-3|(-2x + 3)| + 2) + 5 between the vertical lines x = 1.1 and x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.1
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_098
|
algebra_func_area
|
[
{
"content": "Find the area of the region bounded by the curves f(x) = (2(-2(-1|(4x^2 + 5x + 4) - 2| - 1) - 5) - 3)/(-3(-2(-1|(4x^2 + 5x + 4) - 2| - 1) - 5) + 1), g(x) = -1(-1(1sin(3πx + 1) - 1)^2 + 4(1sin(3πx + 1) - 1) - 2) - 1, x = -1.2, and x = -0.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
11.5
|
math
|
algebra_func_area
|
test_in
|
algebra_func_area_test_in_099
|
algebra_func_area
|
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(5(1((-3x - 3)/(2x - 1))^2 + 3((-3x - 3)/(2x - 1)) + 2) + 1) + 1| and g(x) = 2(3|(-3sin(2πx + 1) + 2) + 1| + 3) - 3 between the vertical lines x = 3.3 and x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12.1
|
math
|
algebra_func_area
|
test_in
|
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