messages listlengths 1 1 | ground_truth stringclasses 50 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 3(-3|(1sin(2π(3((2x - 3)/(2x + 2)) - 4) - 3) - 3) + 2| - 2)^2 + 4(-3|(1sin(2π(3((2x - 3)/(2x + 2)) - 4) - 3) - 3) + 2| - 2) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex forma... | 9 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -4((-2(-1(-3(3|x - 3| - 3)^2 + 1(3|x - 3| - 3)) - 3) + 3)/(-1(-1(-3(3|x - 3| - 3)^2 + 1(3|x - 3| - 3)) - 3) - 3))^2 + 1((-2(-1(-3(3|x - 3| - 3)^2 + 1(3|x - 3| - 3)) - 3) + 3)/(-1(-1(-3(3|x - 3| - 3)^2 + 1(3|... | 2 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -1(-5(-1((3(-2|x - 1| - 1) + 2)/(1(-2|x - 1| - 1) + 3)) - 4)^2 + 5(-1((3(-2|x - 1| - 1) + 2)/(1(-2|x - 1| - 1) + 3)) - 4) - 2) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex form... | 0 | MATH |
[
{
"content": "How many local minima does the function f(x) = -2|((2(-1(-2(-3x^2) + 5) + 5) - 3)/(1(-1(-2(-3x^2) + 5) + 5) + 2)) - 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 x-coordinate of the local extremum with the smallest y-value of the function f(x) = 2|((1(-5(3cos(1π(2|x + 1| + 3) - 2) + 3)) - 3)/(-2(-5(3cos(1π(2|x + 1| + 3) - 2) + 3)) + 1)) + 1| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed... | -1 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum of the function f(x) = -4(3((2(3(-2x + 3)^2 - 1(-2x + 3) + 4) - 1)/(-2(3(-2x + 3)^2 - 1(-2x + 3) + 4) - 2)) + 2)^2 - 5(3((2(3(-2x + 3)^2 - 1(-2x + 3) + 4) - 1)/(-2(3(-2x + 3)^2 - 1(-2x + 3) + 4) - 2)) + 2) - 4 in the interval [-10, 10]. Round to the neare... | 1 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = 3(2e^(-2(-5(-1|(4x^2 + 2x + 3) - 1| + 3) + 5)) + 2)^2 - 1(2e^(-2(-5(-1|(4x^2 + 2x + 3) - 1| + 3) + 5)) + 2) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 4(5((3(3cos(1π(-1x + 3) + 1) - 3) + 2)/(-1(3cos(1π(-1x + 3) + 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}",
... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (2(1e^(-2(-2|(3|(-2|x + 3| - 1) - 3| - 1) + 3| - 2)) - 3))/(3(1e^(-2(-2|(3|(-2|x + 3| - 1) - 3| - 1) + 3| - 2)) - 3) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\b... | -2 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum of the function f(x) = 2|(5(-1(2|(-2e^(2x) + 3) - 2| - 2) + 1)^2 + 5(-1(2|(-2e^(2x) + 3) - 2| - 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 rightmost local extremum of the function f(x) = -1cos(3π(-4(-4(5(-3|x + 3| + 2)^2 - 5(-3|x + 3| + 2) - 2)^2 - 5(5(-3|x + 3| + 2)^2 - 5(-3|x + 3| + 2) - 2))^2 + 3(-4(5(-3|x + 3| + 2)^2 - 5(-3|x + 3| + 2) - 2)^2 - 5(5(-3|x + 3| + 2)^2 - 5(-3|x + 3| + 2) - 2)) - 2)) - 2 i... | -2 | MATH |
[
{
"content": "How many local minima does the function f(x) = 3(-3cos(2π((-1(-3(-2|x - 1|)^2 + 1(-2|x - 1|) - 3))/(-2(-3(-2|x - 1|)^2 + 1(-2|x - 1|) - 3) + 3)) + 3) + 3) - 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 maximum of the function f(x) = (3((-1((1(1(-1sin(2πx - 3) - 2) - 5) + 3)/(3(1(-1sin(2πx - 3) - 2) - 5))))/(2((1(1(-1sin(2πx - 3) - 2) - 5) + 3)/(3(1(-1sin(2πx - 3) - 2) - 5))) + 2)) + 1)/(2((-1((1(1(-1sin(2πx - 3) - 2) - 5) + 3)/(3(1(-1sin(2πx - 3) - 2)... | 9 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 2cos(3π(-1(5(1|(4x - 4) + 1| - 2)^2 - 2)^2 + 1(5(1|(4x - 4) + 1| - 2)^2 - 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... | -1 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 4(3cos(3π(1(-1(1|x + 1| - 2) - 2)^2 - 3(-1(1|x + 1| - 2) - 2) + 2) + 2) - 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 leftmost local maximum of the function f(x) = -1(2|((-2(-1|(-4x^2 + 3x - 3) + 1| + 1) + 2)/(-1(-1|(-4x^2 + 3x - 3) + 1| + 1) - 2)) - 2| + 3)^2 + 3(2|((-2(-1|(-4x^2 + 3x - 3) + 1| + 1) + 2)/(-1(-1|(-4x^2 + 3x - 3) + 1| + 1) - 2)) - 2| + 3) + 2 in the interval [-10, 10].... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 3(2e^(-2(-2|(-1(-1|x + 3| - 1)) - 2| - 2)) - 1)^2 + 1(2e^(-2(-2|(-1(-1|x + 3| - 1)) - 2| - 2)) - 1) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | -4 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -2(-5(3sin(3π(-1|(2|x + 1| + 3) + 1| - 2) - 3)) + 2)^2 - 2(-5(3sin(3π(-1|(2|x + 1| + 3) + 1| - 2) - 3)) + 2) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -3sin(2π((3(1|((3(-1|x - 3| - 3) - 1)/(-1(-1|x - 3| - 3) + 2))| + 2) + 1)/(-1(1|((3(-1|x - 3| - 3) - 1)/(-1(-1|x - 3| - 3) + 2))| + 2) - 3)) - 2) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the a... | -2 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 1|(-1cos(3π(2|(5(4x) - 4) + 1| + 1)) - 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": "How many local minima does the function f(x) = 1|(3((-2(-4((2x + 2)/(-3x + 4)) + 1) - 2)/(3(-4((2x + 2)/(-3x + 4)) + 1) + 2))^2 + 2((-2(-4((2x + 2)/(-3x + 4)) + 1) - 2)/(3(-4((2x + 2)/(-3x + 4)) + 1) + 2)) - 5) + 2| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -2((2(3((3(2x + 4) + 2)/(1(2x + 4)))^2 + 2((3(2x + 4) + 2)/(1(2x + 4))) - 3) + 3)/(2(3((3(2x + 4) + 2)/(1(2x + 4)))^2 + 2((3(2x + 4) + 2)/(1(2x + 4))) - 3) - 1))^2 + 5((2(3((3(2x + 4) + 2)/(1(2x + 4)))^2 +... | -2 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = (-3(-1|((2((-3(-1|x|))/(-1(-1|x|) + 2)) + 3)/(-1((-3(-1|x|))/(-1(-1|x|) + 2)) + 3)) - 1| + 1))/(1(-1|((2((-3(-1|x|))/(-1(-1|x|) + 2)) + 3)/(-1((-3(-1|x|))/(-1(-1|x|) + 2)) + 3)) - 1| + 1) + 1) in the interval [-10, 10]. Round to th... | 0 | MATH |
[
{
"content": "Find the average of all x-coordinates of local minima of the function f(x) = -4(1((-1(-1sin(1π(-3|x + 1|)) - 1) + 3)/(1(-1sin(1π(-3|x + 1|)) - 1) + 3)) - 1) + 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 average of all x-coordinates of local extrema of the function f(x) = (1(2cos(1π(-2(-5(-5x^2 - 2x - 2)^2 + 4(-5x^2 - 2x - 2) - 3)^2 - 3(-5(-5x^2 - 2x - 2)^2 + 4(-5x^2 - 2x - 2) - 3) + 2) + 1) - 2) + 3)/(-1(2cos(1π(-2(-5(-5x^2 - 2x - 2)^2 + 4(-5x^2 - 2x - 2) - 3)^2 - 3(-5(-5x^2 - 2x - 2)^2 ... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 5(-3sin(3π(4((2(-1x^2 + 4x + 5) + 2)/(-2(-1x^2 + 4x + 5) - 3))^2 + 5((2(-1x^2 + 4x + 5) + 2)/(-2(-1x^2 + 4x + 5) - 3)) - 2) + 3) - 1)^2 + 4(-3sin(3π(4((2(-1x^2 + 4x + 5) + 2)/(-2(-1x^2 + 4x + 5) - 3))^2 + 5((2(-1x^2 + 4x +... | -2 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (1(-2(-4(3|(4x^2 - 1x) + 2| + 3)^2 - 1(3|(4x^2 - 1x) + 2| + 3) + 2)^2 + 2(-4(3|(4x^2 - 1x) + 2| + 3)^2 - 1(3|(4x^2 - 1x) + 2| + 3) + 2) + 4) + 2)/(1(-2(-4(3|(4x^2 - 1x) + 2| + 3)^2 - 1(3|(4x^2 - 1x) + 2| + 3... | -9 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -2(1((-2(3(-1cos(3πx + 2) - 1)^2 - 5(-1cos(3πx + 2) - 1) + 3) - 3)/(-2(3(-1cos(3πx + 2) - 1)^2 - 5(-1cos(3πx + 2) - 1) + 3) + 3))^2 + 2((-2(3(-1cos(3πx + 2) - 1)^2 - 5(-1cos(3πx + 2) - 1) + 3) - 3)/(-2(3(-... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = (-1(1(2(5(1x^2 - 2x - 1)^2 + 4(1x^2 - 2x - 1))^2 + 3(5(1x^2 - 2x - 1)^2 + 4(1x^2 - 2x - 1)) + 3)^2 + 3(2(5(1x^2 - 2x - 1)^2 + 4(1x^2 - 2x - 1))^2 + 3(5(1x^2 - 2x - 1)^2 + 4(1x^2 - 2x - 1)) + 3)) + 2)/(1(1(2(5(1x^2 - 2x - 1... | 8 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 3|(-1(3e^(2(2(-2|x + 2| + 2)^2 - 1(-2|x + 2| + 2) + 4)) + 1) - 4) + 2| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | -3 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 2cos(2π((3(2((-2((-3x + 1)/(-1x + 2)) + 2)/(3((-3x + 1)/(-1x + 2)) + 3)) - 4) - 3)/(1(2((-2((-3x + 1)/(-1x + 2)) + 2)/(3((-3x + 1)/(-1x + 2)) + 3)) - 4))) - 1) - 2 in the interval [-10, 10]. Round to the nea... | -6 | MATH |
[
{
"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 1(-2|(4((2(-3|x - 1| + 2) - 3)/(-2(-3|x - 1| + 2) - 2))^2 - 1((2(-3|x - 1| + 2) - 3)/(-2(-3|x - 1| + 2) - 2)) - 4) + 3| + 1) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex for... | 1 | MATH |
[
{
"content": "How many local minima does the function f(x) = (-2(3|(1|((-1(3e^(2x)) + 1)/(1(3e^(2x)) - 3)) - 2| - 3) + 2| + 2) - 1)/(2(3|(1|((-1(3e^(2x)) + 1)/(1(3e^(2x)) - 3)) - 2| - 3) + 2| + 2) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 2|(-2sin(2π(-1(4(1x + 2) + 2) - 5) + 2) - 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 minimum with the smallest y-value of the function f(x) = 4((-1((-3(-1((1x - 2)/(2x - 1)) - 3) - 3)/(-2(-1((1x - 2)/(2x - 1)) - 3) + 3)) + 1)/(2((-3(-1((1x - 2)/(2x - 1)) - 3) - 3)/(-2(-1((1x - 2)/(2x - 1)) - 3) + 3)) + 3))^2 - 1((-1((-3(-1((1x - 2)/(2x - 1)) - 3)... | 1 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = 1|(-2((1((-3(2x^2 - 4x + 4))/(2(2x^2 - 4x + 4) - 1)) - 1)/(-3((-3(2x^2 - 4x + 4))/(2(2x^2 - 4x + 4) - 1)) - 3))^2 + 5((1((-3(2x^2 - 4x + 4))/(2(2x^2 - 4x + 4) - 1)) - 1)/(-3((-3(2x^2 - 4x + 4))/(2(2x^2 - 4x + 4) - 1)) - 3)) + 4) + ... | 1 | MATH |
[
{
"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (3(-3|((-2(3|(-1sin(3πx) + 3) - 1| - 3) - 1)/(-1(3|(-1sin(3πx) + 3) - 1| - 3) - 1)) - 3|) + 1)/(3(-3|((-2(3|(-1sin(3πx) + 3) - 1| - 3) - 1)/(-1(3|(-1sin(3πx) + 3) - 1| - 3) - 1)) - 3|) - 2) in the interval [-10, 10]. Rou... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = -5((-2(-2|(5(4x + 2)^2 + 2(4x + 2) - 5) + 1| + 1) - 1)/(2(-2|(5(4x + 2)^2 + 2(4x + 2) - 5) + 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 |
[
{
"content": "How many local extrema (both minima and maxima) does the function f(x) = (2(1(-4(4(-1|x| - 2)^2 + 3(-1|x| - 2) - 3)^2 - 1(4(-1|x| - 2)^2 + 3(-1|x| - 2) - 3) + 1)^2 - 5(-4(4(-1|x| - 2)^2 + 3(-1|x| - 2) - 3)^2 - 1(4(-1|x| - 2)^2 + 3(-1|x| - 2) - 3) + 1) - 1) - 1)/(3(1(-4(4(-1|x| - 2)^2 + 3(-1|x| - 2... | 77 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum of the function f(x) = -2(-2((-1(3(-1|x + 1| + 1)^2 + 1(-1|x + 1| + 1) + 2) + 3)/(-2(3(-1|x + 1| + 1)^2 + 1(-1|x + 1| + 1) + 2) + 3))^2 + 4((-1(3(-1|x + 1| + 1)^2 + 1(-1|x + 1| + 1) + 2) + 3)/(-2(3(-1|x + 1| + 1)^2 + 1(-1|x + 1| + 1) + 2) + 3)) + 1) + 1 i... | -1 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (-3(-4(3|((1(-2|x + 2| + 1) - 1)/(3(-2|x + 2| + 1) - 2)) - 3|)^2 + 3(3|((1(-2|x + 2| + 1) - 1)/(3(-2|x + 2| + 1) - 2)) - 3|) + 2) + 2)/(-2(-4(3|((1(-2|x + 2| + 1) - 1)/(3(-2|x + 2| + 1) - 2)) - 3|)^2 + 3(3|((1(-2|x + 2| +... | -2 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 4(2(-1|(5(2cos(1πx + 3) - 1)^2 + 3(2cos(1πx + 3) - 1) + 1) - 2| + 2)^2 + 3(-1|(5(2cos(1πx + 3) - 1)^2 + 3(2cos(1πx + 3) - 1) + 1) - 2| + 2) - 5) - 4 in the interval [-10, 10]. Round to the nearest integer.\n... | -9 | MATH |
[
{
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -1e^(-1(-1|(-1|((2(2x - 3) - 1)/(-3(2x - 3) - 3)) - 3| - 3) + 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"
}
] | 1 | MATH |
[
{
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -3|(1sin(2π(-3(-2|(4x + 5)| + 1) - 2) - 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"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -1(-1|(-2|((1(2sin(2πx + 2) - 1) - 2)/(2(2sin(2πx + 2) - 1) - 3))| + 1) - 1| - 1)^2 - 5(-1|(-2|((1(2sin(2πx + 2) - 1) - 2)/(2(2sin(2πx + 2) - 1) - 3))| + 1) - 1| - 1) + 5 in the interval [-10, 10]. Round to ... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum of the function f(x) = 3e^(-1(5(1|(-2|(1|x - 3| - 1) - 2| - 2) + 1| + 2) + 5)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "How many local minima does the function f(x) = 1|(3cos(3π(-2|((-1(2|x + 2| - 3) - 1)/(2(2|x + 2| - 3))) + 2| - 2) - 1) + 1) + 1| + 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 minima does the function f(x) = -2|(-1|(5(-3(-4x^2 + 2x - 4)^2 - 2(-4x^2 + 2x - 4) + 5)^2 + 1(-3(-4x^2 + 2x - 4)^2 - 2(-4x^2 + 2x - 4) + 5) + 3) + 3| + 3) + 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 local maximum with the largest y-value of the function f(x) = 1cos(3π(-4(-1|((2(-1x - 5) - 1)/(-2(-1x - 5))) - 3| - 1)^2 + 5(-1|((2(-1x - 5) - 1)/(-2(-1x - 5))) - 3| - 1)) - 1) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex ... | -9 | MATH |
[
{
"content": "Find the average of all x-coordinates of local minima of the function f(x) = 3|(3sin(3π(-1|((1(5x + 5) - 3)/(-3(5x + 5) + 4)) + 2| - 2) - 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": "user"
}
] | -1 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 3|((-2(-4(1sin(2π((-1x + 3)/(-2x - 2)) + 3) - 2)^2 + 5(1sin(2π((-1x + 3)/(-2x - 2)) + 3) - 2) - 5) - 3)/(-1(-4(1sin(2π((-1x + 3)/(-2x - 2)) + 3) - 2)^2 + 5(1sin(2π((-1x + 3)/(-2x - 2)) + 3) - 2) - 5) + 3)) + 2| + 1 in the i... | -4 | MATH |
[
{
"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 1cos(1π(3(4((2(3x^2 - 4x - 4) + 3)/(-1(3x^2 - 4x - 4) + 2))^2 - 4((2(3x^2 - 4x - 4) + 3)/(-1(3x^2 - 4x - 4) + 2)) + 2) - 2) + 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex... | 1 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = (-1(-1((2(2|(3|x|) + 3|))/(-3(2|(3|x|) + 3|) - 3))^2 - 4((2(2|(3|x|) + 3|))/(-3(2|(3|x|) + 3|) - 3)) - 3) + 1)/(2(-1((2(2|(3|x|) + 3|))/(-3(2|(3|x|) + 3|) - 3))^2 - 4((2(2|(3|x|) + 3|))/(-3(2|(3|x|) + 3|) - 3)) - 3) + 1) in the int... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (-1(3|((2(-4(-3|x - 3| + 2) + 5) + 3)/(1(-4(-3|x - 3| + 2) + 5) + 2)) + 2|))/(-1(3|((2(-4(-3|x - 3| + 2) + 5) + 3)/(1(-4(-3|x - 3| + 2) + 5) + 2)) + 2|) + 3) in the interval [-10, 10]. Round to the nearest ... | 3 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -4(-4(-3|(5((2x - 1)/(-1x - 2)) + 2) + 3| + 3)^2 - 4(-3|(5((2x - 1)/(-1x - 2)) + 2) + 3| + 3) + 1)^2 - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 2 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (-3(4(2cos(3π(3(4x^2 - 2x + 1)^2 + 4(4x^2 - 2x + 1) + 4) + 1) - 3)^2 + 5(2cos(3π(3(4x^2 - 2x + 1)^2 + 4(4x^2 - 2x + 1) + 4) + 1) - 3) - 1) - 2)/(-1(4(2cos(3π(3(4x^2 - 2x + 1)^2 + 4(4x^2 - 2x + 1) + 4) + 1) -... | 0 | MATH |
[
{
"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 1((2(2|((2(-4x - 3) + 2)/(-3(-4x - 3) - 3)) - 1| - 2))/(-1(2|((2(-4x - 3) + 2)/(-3(-4x - 3) - 3)) - 1| - 2) - 2)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 3 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -4(-2|(1(2sin(2π(2|x + 3| - 1) + 1)) - 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": "Find the x-coordinate of the local minimum of the function f(x) = (-3(-1(-2((-3(1x + 4) - 3)/(-2(1x + 4) - 1))^2 - 3((-3(1x + 4) - 3)/(-2(1x + 4) - 1)) - 1)) - 3)/(2(-1(-2((-3(1x + 4) - 3)/(-2(1x + 4) - 1))^2 - 3((-3(1x + 4) - 3)/(-2(1x + 4) - 1)) - 1)) - 1) in the interval [-10, 10]. Round to the... | -5 | MATH |
[
{
"content": "How many local minima does the function f(x) = -1|(5(1((-2(-4x^2 + 1x - 5))/(-3(-4x^2 + 1x - 5) + 4))^2 + 4((-2(-4x^2 + 1x - 5))/(-3(-4x^2 + 1x - 5) + 4)) + 1) + 1) + 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 leftmost local extremum of the function f(x) = -3(-2|(-2(1(3x^2 + 3x - 2)^2 + 5(3x^2 + 3x - 2) - 3) - 4) + 1| - 2)^2 + 4(-2|(-2(1(3x^2 + 3x - 2)^2 + 5(3x^2 + 3x - 2) - 3) - 4) + 1| - 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer ... | -2 | MATH |
[
{
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = (2(-1(-1|(5(2e^(2x) + 2) + 4) - 3| + 2)^2 + 2(-1|(5(2e^(2x) + 2) + 4) - 3| + 2) - 4) + 2)/(-1(-1(-1|(5(2e^(2x) + 2) + 4) - 3| + 2)^2 + 2(-1|(5(2e^(2x) + 2) + 4) - 3| + 2) - 4) + 3) in the interval [-10, 10]. Round to the ... | 6 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1|(1cos(3π(-4((-1((-2x - 3)/(-1x + 3)) - 3)/(2((-2x - 3)/(-1x + 3)) + 3)) + 4))) - 1| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | -4 | MATH |
[
{
"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (-2(-3(-4((-2(3x^2 - 3x - 5) + 3)/(3(3x^2 - 3x - 5) - 1))^2 + 3((-2(3x^2 - 3x - 5) + 3)/(3(3x^2 - 3x - 5) - 1)) + 5) - 5) + 2)/(2(-3(-4((-2(3x^2 - 3x - 5) + 3)/(3(3x^2 - 3x - 5) - 1))^2 + 3((-2(3x^2 - 3x - 5) + 3)/(3(3x^... | 0 | MATH |
[
{
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 2|(-1(2|(-5(3cos(2πx + 2) + 1) + 5) + 1| - 3) + 3)| - 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 extrema (both minima and maxima) does the function f(x) = 2cos(2π(3(2|(-3(5x^2 + 5x + 1) + 4) + 3| - 1) + 1) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 406 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = -3|((-3(-2e^(-1(3|((-1x - 2)/(-2x - 1))| - 2)) - 2) - 1)/(3(-2e^(-1(3|((-1x - 2)/(-2x - 1))| - 2)) - 2) + 3)) - 1| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your ans... | -1 | MATH |
[
{
"content": "How many local minima does the function f(x) = -3(1|(-1((2(-2x) + 1)/(2(-2x) + 3)) + 1) - 1|)^2 - 2(1|(-1((2(-2x) + 1)/(2(-2x) + 3)) + 1) - 1|) + 4 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) = -2(3|((-1(-1(3x - 4)^2 - 4(3x - 4) - 3))/(1(-1(3x - 4)^2 - 4(3x - 4) - 3) - 2))| - 3)^2 + 2(3|((-1(-1(3x - 4)^2 - 4(3x - 4) - 3))/(1(-1(3x - 4)^2 - 4(3x - 4) - 3) - 2))| - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\box... | 0 | MATH |
[
{
"content": "How many local minima does the function f(x) = -1((-2(4((-2(-2cos(1πx - 3) - 1) + 3)/(-2(-2cos(1πx - 3) - 1) + 1)) + 3) + 3)/(-1(4((-2(-2cos(1πx - 3) - 1) + 3)/(-2(-2cos(1πx - 3) - 1) + 1)) + 3) - 2))^2 - 4((-2(4((-2(-2cos(1πx - 3) - 1) + 3)/(-2(-2cos(1πx - 3) - 1) + 1)) + 3) + 3)/(-1(4((-2(-2cos(... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (-3(-3(3(-5((3x)/(1x + 1)) + 5)^2 + 4(-5((3x)/(1x + 1)) + 5) - 2)^2 - 1(3(-5((3x)/(1x + 1)) + 5)^2 + 4(-5((3x)/(1x + 1)) + 5) - 2) + 1) + 1)/(-1(-3(3(-5((3x)/(1x + 1)) + 5)^2 + 4(-5((3x)/(1x + 1)) + 5) - 2... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -3e^(2(2|(-1(1((2x - 3)/(2x)) - 5)^2 - 2) - 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 |
[
{
"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = (-1(2(3|(2cos(2π((3x + 3)/(2x)) + 2) - 2) + 2| - 3) - 5) - 2)/(-3(2(3|(2cos(2π((3x + 3)/(2x)) + 2) - 2) + 2| - 3) - 5) + 4) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\b... | -5 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -1(-1|(-3|(2(1sin(3πx) - 2)^2 + 2) - 2| + 3) - 1|)^2 + 5(-1|(-3|(2(1sin(3πx) - 2)^2 + 2) - 2| + 3) - 1|) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = 2((-2(5((-2((3x + 1)/(2x + 3)) - 2)/(-3((3x + 1)/(2x + 3)) - 2))^2) + 1)/(-2(5((-2((3x + 1)/(2x + 3)) - 2)/(-3((3x + 1)/(2x + 3)) - 2))^2) + 3)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex... | -1 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = (-3(1|(2|((-1(1x^2 + 5) - 2)/(-3(1x^2 + 5) - 3)) + 2|)| + 1) - 1)/(3(1|(2|((-1(1x^2 + 5) - 2)/(-3(1x^2 + 5) - 3)) + 2|)| + 1) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\bo... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (-1((2((2(-4((-2x - 3)/(-2x + 3))^2 + 2((-2x - 3)/(-2x + 3)) - 3))/(-3(-4((-2x - 3)/(-2x + 3))^2 + 2((-2x - 3)/(-2x + 3)) - 3) + 4)) + 3)/(-1((2(-4((-2x - 3)/(-2x + 3))^2 + 2((-2x - 3)/(-2x + 3)) - 3))/(-3(... | -2 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -1(2(-1(4(1sin(2πx + 3))^2 - 4(1sin(2πx + 3)) - 3) + 2)^2 + 5(-1(4(1sin(2πx + 3))^2 - 4(1sin(2πx + 3)) - 3) + 2) + 3)^2 + 3(2(-1(4(1sin(2πx + 3))^2 - 4(1sin(2πx + 3)) - 3) + 2)^2 + 5(-1(4(1sin(2πx + 3))^2 - 4(1sin(2πx + 3... | 10 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 5(3cos(1π(-1|(-1|(-1|x + 2| - 2) - 2| - 2) - 1| - 1) - 1) - 2)^2 + 3(3cos(1π(-1|(-1|(-1|x + 2| - 2) - 2| - 2) - 1| - 1) - 1) - 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the a... | -2 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = (2((1((2(-5(-1|x| - 3) - 3))/(-1(-5(-1|x| - 3) - 3) - 1)) - 2)/(-1((2(-5(-1|x| - 3) - 3))/(-1(-5(-1|x| - 3) - 3) - 1)) + 3)) - 1)/(2((1((2(-5(-1|x| - 3) - 3))/(-1(-5(-1|x| - 3) - 3) - 1)) - 2)/(-1((2(-5(-1|x| - 3) - 3))/(-1(-5(-1|x|... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 4(-5(-2|(-3|(-1x + 2) + 1|) + 2| - 3)^2 - 1(-2|(-3|(-1x + 2) + 1|) + 2| - 3) + 1)^2 + 1(-5(-2|(-3|(-1x + 2) + 1|) + 2| - 3)^2 - 1(-2|(-3|(-1x + 2) + 1|) + 2| - 3) + 1) - 2 in the interval [-10, 10]. Round to... | 2 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (2(-5((-1(-3|(1|x| - 3)| + 1) - 2)/(1(-3|(1|x| - 3)| + 1)))^2 - 5((-1(-3|(1|x| - 3)| + 1) - 2)/(1(-3|(1|x| - 3)| + 1))) - 1) - 1)/(1(-5((-1(-3|(1|x| - 3)| + 1) - 2)/(1(-3|(1|x| - 3)| + 1)))^2 - 5((-1(-3|(1|... | -5 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 3|(2(-4(-2cos(2π(-2|x - 1| + 1) + 1) - 1)^2 + 1(-2cos(2π(-2|x - 1| + 1) + 1) - 1) + 3)^2 + 3(-4(-2cos(2π(-2|x - 1| + 1) + 1) - 1)^2 + 1(-2cos(2π(-2|x - 1| + 1) + 1) - 1) + 3) - 1) - 1| + 2 in the interval [-10, 10]. Round ... | -10 | MATH |
[
{
"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 3(-3(-5(1|(3sin(1πx - 2) + 1)| + 1)^2 - 5(1|(3sin(1πx - 2) + 1)| + 1) - 5)^2 + 2)^2 + 2(-3(-5(1|(3sin(1πx - 2) + 1)| + 1)^2 - 5(1|(3sin(1πx - 2) + 1)| + 1) - 5)^2 + 2) - 3 in the interval [-10, 10]. Round to the nearest ... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 2(4(3cos(3π(1|(4x - 1) + 1| + 1) + 1)) - 1)^2 - 5(4(3cos(3π(1|(4x - 1) + 1| + 1) + 1)) - 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 minimum of the function f(x) = 4((-2((2(4((1x)/(-1x + 2))^2 + 4((1x)/(-1x + 2)) - 2) - 3)/(1(4((1x)/(-1x + 2))^2 + 4((1x)/(-1x + 2)) - 2))) + 1)/(2((2(4((1x)/(-1x + 2))^2 + 4((1x)/(-1x + 2)) - 2) - 3)/(1(4((1x)/(-1x + 2))^2 + 4((1x)/(-1x + 2)) - 2))) + 2)) + 1 in... | 2 | MATH |
[
{
"content": "Find the average of all x-coordinates of local minima of the function f(x) = -3(2sin(3π(2|(-3(2x^2 + 1)^2 + 1(2x^2 + 1) - 2) - 3| + 3) - 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"
}
] | 0 | MATH |
[
{
"content": "How many local minima does the function f(x) = 4(3|(5(1|(2x^2 + 3x) + 1| + 2) + 5) - 2| - 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 x-coordinate of the local minimum with the largest y-value of the function f(x) = 2|((-3(3cos(3π(1(-1x^2 - 2x + 2)^2 + 3) - 1) - 1) + 1)/(2(3cos(3π(1(-1x^2 - 2x + 2)^2 + 3) - 1) - 1) + 1)) - 3| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex for... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -2cos(1π((-3(2|((3((2x)/(-2x - 2)) + 1)/(-1((2x)/(-2x - 2)) + 2)) + 1| - 2) + 1)/(2(2|((3((2x)/(-2x - 2)) + 1)/(-1((2x)/(-2x - 2)) + 2)) + 1| - 2) + 1)) - 3) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\... | 4 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 4(-5(2(-3e^(1((-2x)/(3x - 2))) + 3)^2 - 3(-3e^(1((-2x)/(3x - 2))) + 3) - 1)^2 - 5(2(-3e^(1((-2x)/(3x - 2))) + 3)^2 - 3(-3e^(1((-2x)/(3x - 2))) + 3) - 1) - 1)^2 + 4(-5(2(-3e^(1((-2x)/(3x - 2))) + 3)^2 - 3(-3e... | -1 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = (-1((1((2(-4(1x^2 + 3x) + 1) - 3)/(-2(-4(1x^2 + 3x) + 1) - 2)) - 2)/(-3((2(-4(1x^2 + 3x) + 1) - 3)/(-2(-4(1x^2 + 3x) + 1) - 2)) - 1)))/(3((1((2(-4(1x^2 + 3x) + 1) - 3)/(-2(-4(1x^2 + 3x) + 1) - 2)) - 2)/(-3((2(-4(1x^2 + 3x) + 1) - 3)... | -2 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = (1(-1((1((-3(-2x^2 - 5x + 5))/(-1(-2x^2 - 5x + 5) - 2)) + 2)/(-3((-3(-2x^2 - 5x + 5))/(-1(-2x^2 - 5x + 5) - 2)) + 2))) - 2)/(-2(-1((1((-3(-2x^2 - 5x + 5))/(-1(-2x^2 - 5x + 5) - 2)) + 2)/(-3((-3(-2x^2 - 5x + 5))/(-1(-2x^2 - 5x + 5) -... | -1 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -3|(-2(-1(-1cos(3π((1x)/(2x + 3)) - 3)) - 5)^2 + 4(-1(-1cos(3π((1x)/(2x + 3)) - 3)) - 5) - 4)| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | -6 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 3(-2sin(3π(1(5(-3x^2 - 3x + 5) + 1)^2 + 2(5(-3x^2 - 3x + 5) + 1) + 1) + 2) + 3) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | -3 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -1|(1(2|(3sin(1π(-2x - 5) - 1)) - 2| + 1) + 3) + 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) = -2(2cos(1π((1(-2|((1x + 3)/(-3x - 2)) + 3| - 3) - 3)/(-2(-2|((1x + 3)/(-3x - 2)) + 3| - 3) - 2)))) + 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 extrema (both minima and maxima) does the function f(x) = 4((-1(2sin(3π(-1(4x^2 + 4x + 5)^2 - 1(4x^2 + 4x + 5) - 3) - 2)) - 1)/(-3(2sin(3π(-1(4x^2 + 4x + 5)^2 - 1(4x^2 + 4x + 5) - 3) - 2)) + 1)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your ... | 159 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -2(3((-1(3(5x^2 + 5x + 1)^2 + 1) - 1)/(-1(3(5x^2 + 5x + 1)^2 + 1) + 3)) + 2)^2 - 2(3((-1(3(5x^2 + 5x + 1)^2 + 1) - 1)/(-1(3(5x^2 + 5x + 1)^2 + 1) + 3)) + 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\n... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = (-1(-2((1((-2(1x^2 - 2x - 1) - 1)/(2(1x^2 - 2x - 1) - 3)) - 3)/(1((-2(1x^2 - 2x - 1) - 1)/(2(1x^2 - 2x - 1) - 3)) + 2)) - 5))/(2(-2((1((-2(1x^2 - 2x - 1) - 1)/(2(1x^2 - 2x - 1) - 3)) - 3)/(1((-2(1x^2 - 2x - 1) - 1)/(2(1x^2 - 2x - 1... | 1 | MATH |
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