id
stringlengths 38
38
| setting_key
stringclasses 1
value | setting_name
stringclasses 0
values | messages
listlengths 1
1
| ground_truth
stringclasses 37
values | dataset
stringclasses 1
value |
|---|---|---|---|---|---|
algebra_func_extrema_coords_train_0000
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local maximum of the function f(x) = 3((2(-2x^2 + 4x + 5) - 1)/(1(-2x^2 + 4x + 5))) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
algebra_func_extrema_coords_train_0001
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (1(-2(-3|(5x^2 - 1)| + 2) + 3) - 1)/(1(-2(-3|(5x^2 - 1)| + 2) + 3) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0002
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -3(3sin(3πx - 1))^2 + 4(3sin(3πx - 1)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-10
|
math
|
algebra_func_extrema_coords_train_0003
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -1((2(2|(2cos(3πx - 2) - 1) - 2| + 2) + 2)/(-2(2|(2cos(3πx - 2) - 1) - 2| + 2)))^2 + 1((2(2|(2cos(3πx - 2) - 1) - 2| + 2) + 2)/(-2(2|(2cos(3πx - 2) - 1) - 2| + 2))) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
10
|
math
|
algebra_func_extrema_coords_train_0004
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "How many local minima does the function f(x) = -1(-3|x + 3| + 3)^2 - 2(-3|x + 3| + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0005
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -2sin(3π(2|x| - 1) - 3) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
10
|
math
|
algebra_func_extrema_coords_train_0006
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -3(2cos(3π((3x + 3)/(2x + 1)) - 1) - 3) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
algebra_func_extrema_coords_train_0007
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 4(3cos(1π(1|x| - 1) - 3) - 3)^2 - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0008
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local extremum of the function f(x) = -4(2|(4x^2 + 5x + 2) + 3|) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1
|
math
|
algebra_func_extrema_coords_train_0009
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local extremum of the function f(x) = -5(3((2x - 1)/(3x)))^2 + 4(3((2x - 1)/(3x))) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
algebra_func_extrema_coords_train_0010
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "How many local maxima does the function f(x) = -2((-2(-2|(4x^2 - 3x + 1) + 1| - 1) + 3)/(-2(-2|(4x^2 - 3x + 1) + 1| - 1) + 1)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0011
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local minimum of the function f(x) = (-1(-3|(-3e^(-2(1x^2 - 2x + 1)) - 3) - 3| + 2) - 1)/(-1(-3|(-3e^(-2(1x^2 - 2x + 1)) - 3) - 3| + 2) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
algebra_func_extrema_coords_train_0012
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 3sin(1π((1x - 3)/(2x)) - 3) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
algebra_func_extrema_coords_train_0013
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -5((-2x + 1)/(-3x + 2))^2 + 3((-2x + 1)/(-3x + 2)) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0014
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "How many local minima does the function f(x) = -5((1(-1|(-5x^2 - 1x) - 1| - 3) - 3)/(-2(-1|(-5x^2 - 1x) - 1| - 3) + 3)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0015
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -5(1cos(1πx + 2) - 1)^2 - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
9
|
math
|
algebra_func_extrema_coords_train_0016
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -2(2cos(3πx - 3) - 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-10
|
math
|
algebra_func_extrema_coords_train_0017
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local extremum of the function f(x) = -2(-3e^(2x))^2 - 5(-3e^(2x)) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0018
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "How many local maxima does the function f(x) = 5(2x + 1)^2 + 3(2x + 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0019
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "How many local maxima does the function f(x) = 5((-3x)/(2x + 2))^2 + 4((-3x)/(2x + 2)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0020
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -5((-3(-2(1|x + 2| - 3)^2 + 2(1|x + 2| - 3) + 5))/(2(-2(1|x + 2| - 3)^2 + 2(1|x + 2| - 3) + 5) + 1)) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_extrema_coords_train_0021
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local maximum of the function f(x) = 5(-2x^2 + 2x + 4) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0022
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -5(-2|(2cos(1π(-3x^2 - 3x - 4)) + 2) + 3| + 1) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-10
|
math
|
algebra_func_extrema_coords_train_0023
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "How many local minima does the function f(x) = -2(-2|(-2e^(1(1x^2 - 2x - 4)) - 1) + 2| - 2) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0024
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -3(2sin(1πx + 2) + 2)^2 + 3(2sin(1πx + 2) + 2) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
9
|
math
|
algebra_func_extrema_coords_train_0025
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (2(-1cos(1πx - 2) + 2) - 3)/(2(-1cos(1πx - 2) + 2) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-9
|
math
|
algebra_func_extrema_coords_train_0026
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -2(-1|(1sin(1π((-3x + 2)/(3x - 1)) + 1) + 3) + 1|)^2 - 3(-1|(1sin(1π((-3x + 2)/(3x - 1)) + 1) + 3) + 1|) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0027
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the average of all x-coordinates of local minima of the function f(x) = 3|(-2cos(2πx - 3)) - 2| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0028
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "How many local minima does the function f(x) = 3|(1(-1((1x + 1)/(-1x + 3)) + 1)^2 + 5(-1((1x + 1)/(-1x + 3)) + 1) + 2) + 2| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0029
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local minimum of the function f(x) = -1|(-2cos(2π((-3(-3x^2 - 4x - 5) + 1)/(3(-3x^2 - 4x - 5) - 2))) + 1) + 1| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1
|
math
|
algebra_func_extrema_coords_train_0030
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -1((3(-4(-2|x - 3|)^2 - 2(-2|x - 3|)) - 1)/(2(-4(-2|x - 3|)^2 - 2(-2|x - 3|)) - 1)) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
algebra_func_extrema_coords_train_0031
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (2(5(3cos(3π(-1x - 4) - 3) - 2)^2 + 4))/(2(5(3cos(3π(-1x - 4) - 3) - 2)^2 + 4) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-10
|
math
|
algebra_func_extrema_coords_train_0032
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "How many local extrema (both minima and maxima) does the function f(x) = 1((-3(4(-1|x + 1| + 2)^2 + 4(-1|x + 1| + 2) - 4) + 3)/(3(4(-1|x + 1| + 2)^2 + 4(-1|x + 1| + 2) - 4))) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_extrema_coords_train_0033
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local extremum of the function f(x) = (-3(5(-1|(-1x) - 2|)^2 - 4(-1|(-1x) - 2|) - 5) - 3)/(-2(5(-1|(-1x) - 2|)^2 - 4(-1|(-1x) - 2|) - 5)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-2
|
math
|
algebra_func_extrema_coords_train_0034
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (2(3cos(2π(1x^2 - 1x + 2) + 3) - 2) + 2)/(-2(3cos(2π(1x^2 - 1x + 2) + 3) - 2)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0035
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local maximum of the function f(x) = -3((-1(1(2|x|) + 5) + 2)/(-2(1(2|x|) + 5) - 3))^2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0036
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 2|(5(1sin(2πx - 2) + 2)) + 3| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-9
|
math
|
algebra_func_extrema_coords_train_0037
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 4(3(2|(-1sin(2πx + 1) + 3) - 2|) - 5)^2 + 3(3(2|(-1sin(2πx + 1) + 3) - 2|) - 5) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0038
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 3((-3x - 3)/(-2x - 2)) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
10
|
math
|
algebra_func_extrema_coords_train_0039
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local maximum of the function f(x) = (2(1(-2|x + 1| - 1) + 4) + 1)/(-2(1(-2|x + 1| - 1) + 4) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1
|
math
|
algebra_func_extrema_coords_train_0040
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "How many local maxima does the function f(x) = 2((-1(4x^2 - 3x + 1) - 3)/(1(4x^2 - 3x + 1) + 1)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0041
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "How many local minima does the function f(x) = -1(1|(3((-2x - 2)/(3x - 1)) - 5) - 1| + 2)^2 + 1(1|(3((-2x - 2)/(3x - 1)) - 5) - 1| + 2) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0042
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local minimum of the function f(x) = 1(3x + 2)^2 + 1(3x + 2) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1
|
math
|
algebra_func_extrema_coords_train_0043
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "How many local minima does the function f(x) = -3(3(1e^(1(-1|x|)) - 3) + 1)^2 - 1(3(1e^(1(-1|x|)) - 3) + 1) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0044
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "How many local minima does the function f(x) = 3e^(-2(1(4x^2 - 2x - 2) + 1)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0045
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 1|(-5(-2((1x - 1)/(-2x + 1))^2 - 4((1x - 1)/(-2x + 1)) + 4) + 5) + 2| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0046
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -3((1(2|(-1sin(2πx + 3) + 3) + 2| + 3) + 2)/(-2(2|(-1sin(2πx + 3) + 3) + 2| + 3) - 2)) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-9
|
math
|
algebra_func_extrema_coords_train_0047
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "How many local minima does the function f(x) = -4(-2|((-1(-1x - 2) - 2)/(2(-1x - 2) - 3)) - 1| - 1)^2 - 1(-2|((-1(-1x - 2) - 2)/(2(-1x - 2) - 3)) - 1| - 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0048
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "How many local minima does the function f(x) = -4((-1(-3x - 1) + 1)/(-2(-3x - 1) - 3))^2 - 4((-1(-3x - 1) + 1)/(-2(-3x - 1) - 3)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0049
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 4(-3sin(3π(1x - 4) - 3) + 3)^2 + 1(-3sin(3π(1x - 4) - 3) + 3) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-10
|
math
|
algebra_func_extrema_coords_train_0050
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -1(-2sin(1π(3|x - 1| - 1) + 2)) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
algebra_func_extrema_coords_train_0051
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the average of all x-coordinates of local minima of the function f(x) = 5(-3sin(2πx - 1) + 2) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0052
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local extremum of the function f(x) = -1|((1x - 3)/(1x)) - 2| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0053
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "How many local minima does the function f(x) = -1(3|((-1(2x) - 3)/(3(2x) - 2)) + 3|)^2 + 2(3|((-1(2x) - 3)/(3(2x) - 2)) + 3|) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0054
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (3(-2cos(3π(-4(-2|x - 1|) + 5) - 2) + 3) + 1)/(2(-2cos(3π(-4(-2|x - 1|) + 5) - 2) + 3) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-10
|
math
|
algebra_func_extrema_coords_train_0055
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local extremum of the function f(x) = -1(1e^(1(1|x| + 3)) + 1)^2 + 2(1e^(1(1|x| + 3)) + 1) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0056
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -2|(3cos(3π(-1x^2 - 1x) + 2) + 2) - 2| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-10
|
math
|
algebra_func_extrema_coords_train_0057
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the average of all x-coordinates of local minima of the function f(x) = (1(-1(-3(1e^(2x) + 2)^2 + 1(1e^(2x) + 2) + 2) + 2) + 1)/(-3(-1(-3(1e^(2x) + 2)^2 + 1(1e^(2x) + 2) + 2) + 2) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
9
|
math
|
algebra_func_extrema_coords_train_0058
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -3|((1(-2x^2 + 5x - 2) - 1)/(1(-2x^2 + 5x - 2) + 3)) + 1| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
algebra_func_extrema_coords_train_0059
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "How many local minima does the function f(x) = 1((-1(-1(2|x|)^2 - 4(2|x|) + 4) - 2)/(2(-1(2|x|)^2 - 4(2|x|) + 4) + 3)) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0060
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = (-1(-2|(2sin(2πx) + 2) - 1| + 3) - 1)/(-1(-2|(2sin(2πx) + 2) - 1| + 3) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0061
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local minimum of the function f(x) = 5(-1x - 4)^2 - 5(-1x - 4) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-4
|
math
|
algebra_func_extrema_coords_train_0062
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "How many local maxima does the function f(x) = (-3(-1cos(3πx - 1) + 2) + 3)/(1(-1cos(3πx - 1) + 2) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0063
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -4((2(-3cos(3πx + 3) + 3))/(-2(-3cos(3πx + 3) + 3) + 1)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
10
|
math
|
algebra_func_extrema_coords_train_0064
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local maximum of the function f(x) = (2(1|(-2(5x^2 + 5x - 1) - 5) + 3| + 3) - 2)/(-2(1|(-2(5x^2 + 5x - 1) - 5) + 3| + 3) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0065
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 3((2(-4(1|x - 3| - 1) - 1))/(-3(-4(1|x - 3| - 1) - 1)))^2 - 5((2(-4(1|x - 3| - 1) - 1))/(-3(-4(1|x - 3| - 1) - 1))) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-10
|
math
|
algebra_func_extrema_coords_train_0066
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1(-1cos(3πx - 2) + 3) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-10
|
math
|
algebra_func_extrema_coords_train_0067
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (3(-1cos(3π(1(4x^2 - 5x + 2) - 4)) + 2) + 3)/(-1(-1cos(3π(1(4x^2 - 5x + 2) - 4)) + 2) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
10
|
math
|
algebra_func_extrema_coords_train_0068
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local maximum of the function f(x) = -3|(-4x^2 - 5x - 1) - 3| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1
|
math
|
algebra_func_extrema_coords_train_0069
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "How many local minima does the function f(x) = -5(-1|x - 2| + 3)^2 + 4(-1|x - 2| + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0070
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -2(2sin(3π((-2x + 2)/(2x + 1)) - 3)) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1
|
math
|
algebra_func_extrema_coords_train_0071
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local maximum of the function f(x) = -1(4(-2|x - 3|) - 2)^2 - 4(4(-2|x - 3|) - 2) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
algebra_func_extrema_coords_train_0072
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local extremum of the function f(x) = 3(-1|((-1(-5x^2 - 4x - 1) - 3)/(-3(-5x^2 - 4x - 1) + 4))| + 1) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0073
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1(-2e^(-1(-1x^2 - 4x + 2)) - 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-2
|
math
|
algebra_func_extrema_coords_train_0074
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -5((1(3(-1|x + 1| + 1)^2 + 2(-1|x + 1| + 1) - 4) - 3)/(2(3(-1|x + 1| + 1)^2 + 2(-1|x + 1| + 1) - 4) - 1)) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-2
|
math
|
algebra_func_extrema_coords_train_0075
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local maximum of the function f(x) = -1((-1(2x + 4) + 3)/(-2(2x + 4)))^2 - 1((-1(2x + 4) + 3)/(-2(2x + 4))) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1
|
math
|
algebra_func_extrema_coords_train_0076
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local extremum of the function f(x) = 4(-2e^(1((-1x - 3)/(2x - 1))) - 3) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1
|
math
|
algebra_func_extrema_coords_train_0077
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (-1(-2cos(1πx + 1) + 1) + 1)/(2(-2cos(1πx + 1) + 1) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-8
|
math
|
algebra_func_extrema_coords_train_0078
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "How many local maxima does the function f(x) = 2(-2|(-4(3cos(1πx + 1) - 1)^2 + 1(3cos(1πx + 1) - 1) + 5)| - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0079
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the average of all x-coordinates of local minima of the function f(x) = -2((2(3sin(2πx + 1) + 3) - 1)/(-3(3sin(2πx + 1) + 3) + 1))^2 + 1((2(3sin(2πx + 1) + 3) - 1)/(-3(3sin(2πx + 1) + 3) + 1)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0080
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "How many local minima does the function f(x) = -1|(5x + 2) - 2| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0081
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "How many local maxima does the function f(x) = 1|((-2(-1(-4x^2 + 3x + 4) - 4) + 1)/(-3(-1(-4x^2 + 3x + 4) - 4) + 2)) - 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0082
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 4(1cos(1πx - 1) - 1)^2 - 2(1cos(1πx - 1) - 1) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-10
|
math
|
algebra_func_extrema_coords_train_0083
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "How many local extrema (both minima and maxima) does the function f(x) = -1|(5(3((3x + 1)/(3x + 2))^2 - 5((3x + 1)/(3x + 2)) - 3) + 5) + 3| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
algebra_func_extrema_coords_train_0084
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 2cos(3π((1x + 2)/(3x + 2)) - 3) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-2
|
math
|
algebra_func_extrema_coords_train_0085
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -3(-1|(-3sin(1πx - 3) - 3)| + 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-10
|
math
|
algebra_func_extrema_coords_train_0086
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 5(-1sin(2πx - 1) + 1)^2 + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-9
|
math
|
algebra_func_extrema_coords_train_0087
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local extremum of the function f(x) = -5(2|x| + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0088
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the average of all x-coordinates of local minima of the function f(x) = 3(2sin(3πx) - 2) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0089
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -3sin(2π((1x + 2)/(1x - 3)) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-3
|
math
|
algebra_func_extrema_coords_train_0090
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 1sin(1π(2|((-1(-5x^2 - 4x + 2))/(-2(-5x^2 - 4x + 2) - 1)) - 1| - 2) + 2) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-2
|
math
|
algebra_func_extrema_coords_train_0091
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -2((1x + 1)/(-2x - 1))^2 - 1((1x + 1)/(-2x - 1)) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-2
|
math
|
algebra_func_extrema_coords_train_0092
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 5(-2cos(2πx - 1) - 1) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-10
|
math
|
algebra_func_extrema_coords_train_0093
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "How many local maxima does the function f(x) = 2|(1(5x^2 + 2x - 3) + 3) + 2| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0094
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "How many local minima does the function f(x) = -4(2x^2 - 3x - 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0095
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -3cos(2π(-1|x - 3| + 2)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-10
|
math
|
algebra_func_extrema_coords_train_0096
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the average of all x-coordinates of local minima of the function f(x) = 4(-2(1cos(3π(2|x - 3| - 2) - 2) - 2)^2 - 4(1cos(3π(2|x - 3| - 2) - 2) - 2) + 3) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0097
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the local maximum of the function f(x) = (2(-1(-1e^(1x) + 3)^2 + 5(-1e^(1x) + 3) - 4) - 3)/(-1(-1(-1e^(1x) + 3)^2 + 5(-1e^(1x) + 3) - 4) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-1
|
math
|
algebra_func_extrema_coords_train_0098
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 2(-3|(2sin(2π(3x^2 - 3x - 3) - 2) + 2) + 3| - 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
algebra_func_extrema_coords_train_0099
|
algebra_func_extrema_coords
| null |
[
{
"role": "user",
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1(-1(-1|x - 3| + 2)^2 - 3(-1|x - 3| + 2) - 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0
|
math
|
End of preview. Expand
in Data Studio
README.md exists but content is empty.
- Downloads last month
- 7