messages listlengths 1 1 | ground_truth stringclasses 16 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -2((1(-3|x - 3| + 3) - 2)/(1(-3|x - 3| + 3) - 3))^2 + 3((1(-3|x - 3| + 3) - 2)/(1(-3|x - 3| + 3) - 3)) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 3 | MATH |
[
{
"content": "How many local minima does the function f(x) = (-2(3|(5x^2 + 3x + 5) + 1| + 3) - 3)/(1(3|(5x^2 + 3x + 5) + 1| + 3) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 4(-3sin(1πx - 1) - 1)^2 + 5(-3sin(1πx - 1) - 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "Find the average of all x-coordinates of local minima of the function f(x) = (-1(-3cos(2πx - 3) - 3) - 3)/(3(-3cos(2πx - 3) - 3) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 5((2(2x^2 + 1x + 2) + 1)/(-3(2x^2 + 1x + 2) + 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -3((2(3cos(2πx - 3) - 2) - 1)/(1(3cos(2πx - 3) - 2) - 2)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = -2(-2x - 1)^2 - 2(-2x - 1) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = -1(-5x + 4)^2 + 5(-5x + 4) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 3sin(1π(-5(3((-1x + 1)/(-3x))^2 + 1((-1x + 1)/(-3x)) - 5) + 1) - 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4 | MATH |
[
{
"content": "Find the average of all x-coordinates of local minima of the function f(x) = 5((3(2e^(2(-2|x - 3| + 2)) + 3) + 1)/(1(2e^(2(-2|x - 3| + 2)) + 3) + 3)) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -1|(2cos(1πx + 1) + 3) + 2| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -9 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (-2(-3|(1(-5x - 2)^2 + 5(-5x - 2) + 3) - 1| + 2) + 3)/(1(-3|(1(-5x - 2)^2 + 5(-5x - 2) + 3) - 1| + 2) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\b... | 0 | MATH |
[
{
"content": "How many local minima does the function f(x) = -2|(-3(-5x^2 + 1x) - 2) + 3| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -1(-1(1|x + 1| - 2)^2 + 1(1|x + 1| - 2) - 5) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4 | MATH |
[
{
"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 2|(-2((-2x + 1)/(1x - 3))^2 + 2((-2x + 1)/(1x - 3)) + 2) + 3| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 5((-2x - 2)/(-3x + 2))^2 - 5((-2x - 2)/(-3x + 2)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -2(-3|x - 3|)^2 - 1(-3|x - 3|) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1cos(1π(1|((-1x - 2)/(-2x - 2)) + 1| - 1)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | MATH |
[
{
"content": "Find the average of all x-coordinates of local minima of the function f(x) = -1sin(2π(3((1(-5x^2 - 4x + 3) - 2)/(3(-5x^2 - 4x + 3) + 2)) - 1) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = (-1(-2(-2x)^2 + 3(-2x) + 3) + 3)/(-1(-2(-2x)^2 + 3(-2x) + 3)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 1e^(2((2(3|x + 3| - 2) - 3)/(-3(3|x + 3| - 2)))) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -1(-2sin(2πx) - 1) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = (-3(1(-3x^2 + 3x - 5) - 5) + 2)/(1(1(-3x^2 + 3x - 5) - 5)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -1e^(-2(-5x^2 + 1x + 4)) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 5(-2|(-1(-3cos(3πx - 2) + 2)^2 - 4(-3cos(3πx - 2) + 2) + 4)| + 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -4(-3cos(1π(-1|(-1x^2 - 5x - 5)| + 3) + 1) + 1) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = -3(3((-3(1|x| + 2))/(-1(1|x| + 2) + 3)) + 3)^2 - 4(3((-3(1|x| + 2))/(-1(1|x| + 2) + 3)) + 3) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -1(-2|x + 3| + 3)^2 + 5(-2|x + 3| + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 1cos(1π(-2(2x)^2 - 3(2x) + 2) + 3) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = 5(-3|x + 1|)^2 - 1(-3|x + 1|) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = 3((-1(1|(-1e^(-2x)) + 1| - 2) + 1)/(1(1|(-1e^(-2x)) + 1| - 2))) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum of the function f(x) = -3|((1(2(-1x + 5)^2 - 4(-1x + 5) + 5) - 1)/(-2(2(-1x + 5)^2 - 4(-1x + 5) + 5) - 3)) + 1| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 4 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 2cos(3π(-2x^2 + 2x + 1) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -1|(5((-1x + 2)/(-2x + 3))^2 + 2((-1x + 2)/(-2x + 3)) - 3) - 2| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 2(-2sin(1π(3|(1x - 3) - 3| + 1) + 2) - 3)^2 + 3(-2sin(1π(3|(1x - 3) - 3| + 1) + 2) - 3) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 10 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = -1(-5x - 5)^2 - 3(-5x - 5) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = 5(-4x^2 + 2x - 3) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = 4(-1x - 1)^2 + 1(-1x - 1) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "Find the average of all x-coordinates of local minima of the function f(x) = (-2(3cos(1πx - 2) + 3) + 2)/(1(3cos(1πx - 2) + 3)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum of the function f(x) = 1e^(-1(-5x^2 + 4)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "How many local minima does the function f(x) = -5(-1|(3((2x - 1)/(-2x))^2 + 4((2x - 1)/(-2x)) - 4) + 3| + 2) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -2e^(1((3(-5x^2 + 3x + 4) + 3)/(2(-5x^2 + 3x + 4) - 1))) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 2sin(1π(2((2x + 1)/(1x + 1))) + 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -3|((2(-1(3x - 1)^2 - 1(3x - 1) + 3) - 3)/(2(-1(3x - 1)^2 - 1(3x - 1) + 3) + 3)) + 3| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = 4((1(-3x^2 - 3x - 5) + 2)/(1(-3x^2 - 3x - 5) - 3)) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = (2(-2|x + 2| + 2) + 2)/(-3(-2|x + 2| + 2)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | MATH |
[
{
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 1(2cos(1πx - 3) + 1) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -4(2sin(1π((2x - 1)/(-3x - 3)) + 1) - 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -8 | MATH |
[
{
"content": "How many local minima does the function f(x) = -5((1(1|(3x^2 - 4x) - 2|) - 3)/(-1(1|(3x^2 - 4x) - 2|) - 2)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the average of all x-coordinates of local minima of the function f(x) = 1(-2|(3sin(2πx - 1) - 1) - 1| - 3)^2 + 3(-2|(3sin(2πx - 1) - 1) - 1| - 3) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "How many local minima does the function f(x) = -4(-1|((2(-1x - 4) + 2)/(3(-1x - 4) - 1)) + 3| + 3)^2 - 4(-1|((2(-1x - 4) + 2)/(3(-1x - 4) - 1)) + 3| + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 2(-3|(-1sin(1π((1x - 1)/(1x + 1)) + 3) + 3) - 3| - 3)^2 - 1(-3|(-1sin(1π((1x - 1)/(1x + 1)) + 3) + 3) - 3| - 3) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Y... | 3 | MATH |
[
{
"content": "How many local minima does the function f(x) = 4(-2e^(1(-2|((3x + 1)/(2x + 2)) + 2|))) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (-1(1cos(2πx - 1) + 2) - 3)/(-2(1cos(2πx - 1) + 2) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 2(3sin(1πx) - 2)^2 + 4(3sin(1πx) - 2) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (-1(1(-2|x + 3|) + 3) - 1)/(-2(1(-2|x + 3|) + 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 1((1(-4x^2 - 5x + 1) - 2)/(-1(-4x^2 - 5x + 1) - 2)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 2sin(2π(-2x^2 + 2x - 3) - 3) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1(1cos(2π((-1(-5x + 4) - 2)/(-3(-5x + 4) - 3)) + 3) - 2)^2 - 3(1cos(2π((-1(-5x + 4) - 2)/(-3(-5x + 4) - 3)) + 3) - 2) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\bo... | 1 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = 4((-3(-1|x - 2| + 1) + 3)/(-2(-1|x - 2| + 1) + 1)) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many local minima does the function f(x) = -3|(4(3x^2 - 5x + 2) + 3) - 2| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 1cos(1π(-3|x + 3| + 2) + 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 3|((3(-2cos(2π(-4x - 5) - 1) + 3) + 1)/(-2(-2cos(2π(-4x - 5) - 1) + 3) + 1)) - 2| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | -10 | MATH |
[
{
"content": "How many local minima does the function f(x) = -1(-2e^(-2((2x - 1)/(-1x))) + 1)^2 + 3(-2e^(-2((2x - 1)/(-1x))) + 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "How many local minima does the function f(x) = -3|(4(-4((3x + 2)/(1x + 2)) - 4)^2 - 1(-4((3x + 2)/(1x + 2)) - 4) + 5) + 3| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -3(2|(-4x^2 + 3x + 5) - 2| + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = 1(-3x - 1)^2 - 5(-3x - 1) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (-3(3(3|(-1x^2 - 5x + 2) + 3|) + 4) + 3)/(-3(3(3|(-1x^2 - 5x + 2) + 3|) + 4) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | -2 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = 1(-5x - 5)^2 - 5(-5x - 5) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | MATH |
[
{
"content": "How many local minima does the function f(x) = 2|((3(4(2x - 1)^2 + 3) - 2)/(-3(4(2x - 1)^2 + 3) + 1)) + 2| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 3sin(2π(-2x^2 + 5x - 4) + 1) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -1|(-3((1(2x - 3) - 2)/(1(2x - 3) + 3))^2 + 2((1(2x - 3) - 2)/(1(2x - 3) + 3)) - 1) + 1| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the average of all x-coordinates of local minima of the function f(x) = -1(-2cos(1πx - 3) + 3)^2 - 3(-2cos(1πx - 3) + 3) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 4(-4(-2|x - 2| + 2)^2 + 5(-2|x - 2| + 2) + 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "How many local extrema (both minima and maxima) does the function f(x) = 1|(5((-2(-4x^2 + 1x + 3) + 1)/(1(-4x^2 + 1x + 3) + 1)) - 1) - 3| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many local extrema (both minima and maxima) does the function f(x) = -2e^(-1((-1(-2(1|x + 1| - 3) - 2) - 2)/(1(-2(1|x + 1| - 3) - 2) - 2))) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 1cos(1π(-4x - 2) + 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 1(3x^2 - 1x - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -1(2cos(3πx) - 3) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = -3(3e^(1x) - 2)^2 + 3(3e^(1x) - 2) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -3(-2cos(2πx + 1) - 3) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "How many local extrema (both minima and maxima) does the function f(x) = -2cos(2π(-2|((-2x + 3)/(-1x - 3)) - 3| + 2) - 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (3(-1e^(-1(-3|x - 2| - 3)) + 3) + 1)/(2(-1e^(-1(-3|x - 2| - 3)) + 3)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 3e^(2(-3|((-3(2x + 3) - 3)/(-1(2x + 3) - 2)) - 2| + 3)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 2e^(-1(-4x^2 + 2x + 2)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum of the function f(x) = (3(-5(1|(-2x^2 + 1)|) + 3) - 1)/(3(-5(1|(-2x^2 + 1)|) + 3) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = 5((-3(2|(1e^(-1x) - 2) + 3| - 3))/(1(2|(1e^(-1x) - 2) + 3| - 3) + 3))^2 + 1((-3(2|(1e^(-1x) - 2) + 3| - 3))/(1(2|(1e^(-1x) - 2) + 3| - 3) + 3)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in L... | 1 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (1(2(-1sin(1πx - 3) + 3) - 2) + 1)/(-1(2(-1sin(1πx - 3) + 3) - 2) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | -10 | MATH |
[
{
"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -1(-1(-3|x + 3| + 3) - 1)^2 + 5(-1(-3|x + 3| + 3) - 1) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4 | MATH |
[
{
"content": "How many local minima does the function f(x) = -2e^(-1(-5x^2 - 3x + 2)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = (1(1(3x^2 - 4x + 1) - 2) + 1)/(1(1(3x^2 - 4x + 1) - 2) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -3|((2x - 2)/(3x)) + 2| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = (3(-4x^2 + 1x - 3) + 2)/(1(-4x^2 + 1x - 3) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = 1e^(1(3(1|(-1x - 3) + 2| - 1)^2 + 1(1|(-1x - 3) + 2| - 1) - 1)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -8 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = 5(1x^2 + 3x - 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = -3|(-4(3((2x - 2)/(-3x + 2)) + 2)^2 + 4(3((2x - 2)/(-3x + 2)) + 2) - 5) + 1| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 1(2(1|((2x + 1)/(-3x - 3)) - 1| - 3) + 1)^2 - 4(2(1|((2x + 1)/(-3x - 3)) - 1| - 3) + 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answe... | -1 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -3|(-3sin(3π((2x - 3)/(-1x - 1)) + 2) + 2) - 1| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -8 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 2|(-3sin(3πx + 1) + 2) + 3| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum of the function f(x) = 1((-3x - 1)/(1x + 2))^2 + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
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