messages listlengths 1 1 | ground_truth stringclasses 42
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (-1(-1|(-3(-2sin(2πx - 1) - 3)^2 + 3(-2sin(2πx - 1) - 3) + 4)| - 3) + 1)/(2(-1|(-3(-2sin(2πx - 1) - 3)^2 + 3(-2sin(2πx - 1) - 3) + 4)| - 3) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPr... | -9 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum of the function f(x) = -1|((2(3cos(1π(-4x^2 - 4x + 5) - 3) - 2) + 2)/(-2(3cos(1π(-4x^2 - 4x + 5) - 3) - 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 extremum of the function f(x) = 2((-1(-1cos(2π(3|x + 2| - 1) + 2) - 1) + 1)/(-1(-1cos(2π(3|x + 2| - 1) + 2) - 1) + 2))^2 - 2((-1(-1cos(2π(3|x + 2| - 1) + 2) - 1) + 1)/(-1(-1cos(2π(3|x + 2| - 1) + 2) - 1) + 2)) + 5 in the interval [-10, 10]. Round to the ... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (3(5(3sin(1π(2|x|) + 1) - 2)^2 + 5(3sin(1π(2|x|) + 1) - 2) - 1) + 3)/(2(5(3sin(1π(2|x|) + 1) - 2)^2 + 5(3sin(1π(2|x|) + 1) - 2) - 1) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent t... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = (1(-4(-3cos(2π(-3|x + 1| - 1) + 3) + 1)^2 - 1(-3cos(2π(-3|x + 1| - 1) + 3) + 1)) - 2)/(2(-4(-3cos(2π(-3|x + 1| - 1) + 3) + 1)^2 - 1(-3cos(2π(-3|x + 1| - 1) + 3) + 1)) + 1) in the interval [-10, 10]. Round to the nearest int... | -10 | MATH |
[
{
"content": "Find the average of all x-coordinates of local minima of the function f(x) = 1|(-1cos(3π((-3(-1x^2 - 4x + 2))/(3(-1x^2 - 4x + 2) + 2)) - 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"
}
] | -2 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 4((-3(3cos(1π(1|x - 2|)) + 2) - 2)/(3(3cos(1π(1|x - 2|)) + 2) + 3))^2 + 1((-3(3cos(1π(1|x - 2|)) + 2) - 2)/(3(3cos(1π(1|x - 2|)) + 2) + 3)) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPr... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (1(2|(2cos(2π(-4x^2 - 3) + 2) - 1) + 1|))/(2(2|(2cos(2π(-4x^2 - 3) + 2) - 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 |
[
{
"content": "Find the average of all x-coordinates of local minima of the function f(x) = 2|((1(-1cos(2π(4x^2 - 3x + 3) + 2) + 3) - 1)/(-3(-1cos(2π(4x^2 - 3x + 3) + 2) + 3) - 3)) + 2| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 0 | MATH |
[
{
"content": "How many local minima does the function f(x) = -2|((3(2sin(3π(1x^2 - 5x - 3) + 3) + 1) + 1)/(3(2sin(3π(1x^2 - 5x - 3) + 3) + 1) + 2)) - 1| + 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 extrema (both minima and maxima) does the function f(x) = (-3(-2cos(3π(3|(2x^2 - 2x - 5) - 1|) + 1) + 1) - 1)/(2(-2cos(3π(3|(2x^2 - 2x - 5) - 1|) + 1) + 1) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 499 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 3|(-3sin(3π(-1((2x + 1)/(-3x + 1))^2 - 4) + 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"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -1sin(1π(3(-2|((2x + 3)/(-3x - 1)) - 3| + 2)^2 - 1(-2|((2x + 3)/(-3x - 1)) - 3| + 2) + 3) - 1) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | -9 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -5(2|(2cos(3π((3x - 1)/(-2x - 1)) + 2) - 1) + 3| - 1)^2 - 3(2|(2cos(3π((3x - 1)/(-2x - 1)) + 2) - 1) + 3| - 1) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your... | -4 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = -2|(2sin(2π(-2((3x - 2)/(1x - 3))^2 + 5((3x - 2)/(1x - 3)) - 2) + 1) - 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"
}
] | -1 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 5(-1|((-2(2cos(2πx + 2) + 3) + 2)/(-2(2cos(2πx + 2) + 3))) + 1| - 3)^2 + 2(-1|((-2(2cos(2πx + 2) + 3) + 2)/(-2(2cos(2πx + 2) + 3))) + 1| - 3) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nP... | -9 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (-1(5(3|(3cos(1πx - 2) - 2) + 3|)^2 - 3(3|(3cos(1πx - 2) - 2) + 3|) - 5) - 3)/(1(5(3|(3cos(1πx - 2) - 2) + 3|)^2 - 3(3|(3cos(1πx - 2) - 2) + 3|) - 5)) in the interval [-10, 10]. Round to the nearest integer... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (-3(-1(-2|(-3sin(1πx + 3) + 1) + 2| + 2)^2 + 2(-2|(-3sin(1πx + 3) + 1) + 2| + 2) - 1) + 1)/(-2(-1(-2|(-3sin(1πx + 3) + 1) + 2| + 2)^2 + 2(-2|(-3sin(1πx + 3) + 1) + 2| + 2) - 1)) in the interval [-10, 10]. Ro... | -8 | MATH |
[
{
"content": "Find the average of all x-coordinates of local minima of the function f(x) = 1|(1((3(2sin(3πx - 3)) + 2)/(2(2sin(3πx - 3)) + 1))^2 + 4((3(2sin(3πx - 3)) + 2)/(2(2sin(3πx - 3)) + 1)) + 5) + 3| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxe... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -3sin(3π(5((-3(2|x| - 2) + 3)/(-2(2|x| - 2) + 3))^2 + 3((-3(2|x| - 2) + 3)/(-2(2|x| - 2) + 3)) + 3) - 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answe... | -7 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (2(-1|(2(-2sin(2πx - 2) - 1)^2 + 3(-2sin(2πx - 2) - 1) + 1) + 1| - 2) - 1)/(1(-1|(2(-2sin(2πx - 2) - 1)^2 + 3(-2sin(2πx - 2) - 1) + 1) + 1| - 2) + 2) in the interval [-10, 10]. Round to the nearest integer.\... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -3((-3(-3|(1cos(1πx - 1) + 1) + 3| - 3) - 2)/(-3(-3|(1cos(1πx - 1) + 1) + 3| - 3)))^2 - 1((-3(-3|(1cos(1πx - 1) + 1) + 3| - 3) - 2)/(-3(-3|(1cos(1πx - 1) + 1) + 3| - 3))) + 2 in the interval [-10, 10]. Round to the nearest ... | -9 | MATH |
[
{
"content": "How many local extrema (both minima and maxima) does the function f(x) = 1|((-2(5(1cos(1πx + 1))^2 - 1(1cos(1πx + 1)) - 4) - 3)/(-2(5(1cos(1πx + 1))^2 - 1(1cos(1πx + 1)) - 4) - 2)) + 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 71 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -2|(1sin(2π((-2(5x^2 - 3) - 1)/(-2(5x^2 - 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"
}
] | -1 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -3cos(1π(-2|((2(-2x^2 + 3x) + 2)/(1(-2x^2 + 3x) - 2)) + 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"... | -2 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -1sin(3π((-1(3|(1x^2 - 2) - 3| - 3) + 1)/(-1(3|(1x^2 - 2) - 3| - 3) - 2)) + 1) + 3 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 rightmost local extremum of the function f(x) = -2cos(2π(-3((-2(1|x - 3| - 3))/(-2(1|x - 3| - 3) - 2))^2 + 1((-2(1|x - 3| - 3))/(-2(1|x - 3| - 3) - 2)) + 1) + 3) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed... | 9 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 2sin(1π((-1(-1|(3x^2 - 2x - 4) + 2| + 2) + 3)/(-3(-1|(3x^2 - 2x - 4) + 2| + 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 |
[
{
"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -1cos(3π(5(-1|((2x + 3)/(-3x + 2)) + 3|)^2 - 4(-1|((2x + 3)/(-3x + 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... | -9 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -2cos(1π(-4((-3(2|x + 1| + 1) - 1)/(-1(2|x + 1| + 1) - 2))^2 + 4((-3(2|x + 1| + 1) - 1)/(-1(2|x + 1| + 1) - 2)) - 3)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\bo... | 9 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (-3(-5(3|(-3sin(3πx - 3) + 3) - 1| - 1)^2 - 4(3|(-3sin(3πx - 3) + 3) - 1| - 1) + 2) - 2)/(2(-5(3|(-3sin(3πx - 3) + 3) - 1| - 1)^2 - 4(3|(-3sin(3πx - 3) + 3) - 1| - 1) + 2) + 2) in the interval [-10, 10]. Round to the near... | 10 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 2cos(2π(3|((2(-1x^2 - 2x + 5) - 3)/(-1(-1x^2 - 2x + 5) - 3)) - 1| + 1) - 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | -1 | MATH |
[
{
"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -1|(-3cos(1π(-2((1x + 2)/(3x - 2))^2 + 2((1x + 2)/(3x - 2)) - 2) + 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"
... | 1 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -3|((-1(4(1cos(2πx - 1) - 1)^2 + 3(1cos(2πx - 1) - 1) + 1) + 1)/(1(4(1cos(2πx - 1) - 1)^2 + 3(1cos(2πx - 1) - 1) + 1) + 1)) - 3| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex f... | 9 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 3|(4(-1sin(1π((-1x)/(-2x + 3)) + 2) - 2)^2 + 1(-1sin(1π((-1x)/(-2x + 3)) + 2) - 2) + 3) - 3| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your... | 1 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 4(-1|(-1cos(1π((-3x - 1)/(-3x - 2)) - 3)) - 2|)^2 - 4(-1|(-1cos(1π((-3x - 1)/(-3x - 2)) - 3)) - 2|) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxe... | -1 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 1((1(-2|(2cos(3πx + 2) + 3) + 2|) + 1)/(2(-2|(2cos(3πx + 2) + 3) + 2|) + 1))^2 - 1((1(-2|(2cos(3πx + 2) + 3) + 2|) + 1)/(2(-2|(2cos(3πx + 2) + 3) + 2|) + 1)) in the interval [-10, 10]. Round to the nearest integer.\n\nPrese... | -10 | MATH |
[
{
"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 1sin(3π(-2(-2|((-1x + 3)/(2x - 1)) - 1| - 2)^2 + 1(-2|((-1x + 3)/(2x - 1)) - 1| - 2) + 2) + 1) + 2 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 average of all x-coordinates of local extrema of the function f(x) = 2(1|((3(1sin(3πx + 3) + 2) - 3)/(-2(1sin(3πx + 3) + 2) - 3))| + 1)^2 - 5(1|((3(1sin(3πx + 3) + 2) - 3)/(-2(1sin(3πx + 3) + 2) - 3))| + 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -5(-3|(-1cos(3π((-2x - 3)/(1x - 3)) + 2) - 1) - 2| + 3)^2 + 3(-3|(-1cos(3π((-2x - 3)/(1x - 3)) + 2) - 1) - 2| + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex for... | -8 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 1((2(1|(2cos(1πx - 2)) - 3| - 3) - 2)/(-1(1|(2cos(1πx - 2)) - 3| - 3) + 2))^2 + 3((2(1|(2cos(1πx - 2)) - 3| - 3) - 2)/(-1(1|(2cos(1πx - 2)) - 3| - 3) + 2)) + 3 in the interval [-10, 10]. Round to the nearest... | -9 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 3cos(1π((1(-3(1|x + 1|)^2 + 1(1|x + 1|) + 3) + 1)/(1(-3(1|x + 1|)^2 + 1(1|x + 1|) + 3) + 3)) - 3) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | -3 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -2sin(2π((-1(-3(-1|x - 2| + 3)^2 + 1(-1|x - 2| + 3) + 3) + 3)/(-2(-3(-1|x - 2| + 3)^2 + 1(-1|x - 2| + 3) + 3) - 3)) + 2) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer i... | -3 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 1sin(2π(-3((1(1|x + 3| + 1) - 1)/(1(1|x + 3| + 1) + 3))^2 - 1((1(1|x + 3| + 1) - 1)/(1(1|x + 3| + 1) + 3))) - 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex f... | -9 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 2(-2|(-1cos(3π((3x - 1)/(1x + 2)) + 1) + 1) + 3| + 2)^2 + 1(-2|(-1cos(3π((3x - 1)/(1x + 2)) + 1) + 1) + 3| + 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{You... | -8 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = (1(-2|(2cos(2π(-5x^2 + 5x + 3) + 2) + 1) - 1|) - 1)/(3(-2|(2cos(2π(-5x^2 + 5x + 3) + 2) + 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 |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 2sin(1π((2(3|(-2x^2 + 4x - 3)| + 3) - 2)/(-1(3|(-2x^2 + 4x - 3)| + 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"
}... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 1sin(1π(-1|((-3(-4x^2 + 4x) - 2)/(-1(-4x^2 + 4x) + 2)) + 2| + 3) + 2) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 2|(4(2cos(3π((-2x + 2)/(1x)) - 1))^2 + 3(2cos(3π((-2x + 2)/(1x)) - 1)) - 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"
... | -9 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = (2(2(-1cos(3π(-3|x + 2| + 2)) - 2)^2 - 5(-1cos(3π(-3|x + 2| + 2)) - 2) - 1) - 1)/(-2(2(-1cos(3π(-3|x + 2| + 2)) - 2)^2 - 5(-1cos(3π(-3|x + 2| + 2)) - 2) - 1) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\n... | -10 | MATH |
[
{
"content": "Find the average of all x-coordinates of local minima of the function f(x) = 1cos(1π(-1|(-3((-3x - 3)/(1x))^2 + 4((-3x - 3)/(1x)) + 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 x-coordinate of the leftmost local extremum of the function f(x) = -3(1sin(3π((3(3|x - 3| + 3) + 2)/(-3(3|x - 3| + 3) - 3)) - 1))^2 + 3(1sin(3π((3(3|x - 3| + 3) + 2)/(-3(3|x - 3| + 3) - 3)) - 1)) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex f... | 2 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -1sin(3π((-3(-4(-1|x + 3| - 1)^2 + 1(-1|x + 3| - 1)))/(-2(-4(-1|x + 3| - 1)^2 + 1(-1|x + 3| - 1)))) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 9 | MATH |
[
{
"content": "Find the average of all x-coordinates of local minima of the function f(x) = -1|((-2(-1sin(1π(5x^2 + 2x - 4) + 2) - 2) + 3)/(-2(-1sin(1π(5x^2 + 2x - 4) + 2) - 2) + 1)) - 1| + 1 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 average of all x-coordinates of local maxima of the function f(x) = 2|(1sin(1π(-1((-2x - 1)/(1x - 3))^2 - 4((-2x - 1)/(1x - 3)) - 1) - 2) + 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"... | 3 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 3(3|((1(-1cos(1πx + 3) + 3) - 1)/(3(-1cos(1πx + 3) + 3) + 2)) + 3| + 2)^2 + 4(3|((1(-1cos(1πx + 3) + 3) - 1)/(3(-1cos(1πx + 3) + 3) + 2)) + 3| + 2) + 4 in the interval [-10, 10]. Round to the nearest intege... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -4(3|((3(2sin(3πx - 3) + 2) - 2)/(-1(2sin(3πx - 3) + 2) + 2)) - 1|)^2 - 1(3|((3(2sin(3πx - 3) + 2) - 2)/(-1(2sin(3πx - 3) + 2) + 2)) - 1|) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPres... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -3cos(3π((2(-2|(-3x^2 - 4x + 3)| + 2) + 1)/(2(-2|(-3x^2 - 4x + 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}",
... | -2 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -3|((2(-2sin(2π(-5x^2 - 2x + 4) + 2) + 3) + 1)/(-3(-2sin(2π(-5x^2 - 2x + 4) + 2) + 3) - 3)) - 1| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Y... | -10 | MATH |
[
{
"content": "Find the average of all x-coordinates of local minima of the function f(x) = -2(2sin(1π((1(-2|x + 2|) + 1)/(1(-2|x + 2|) + 3)) + 2) + 2)^2 + 1(2sin(1π((1(-2|x + 2|) + 1)/(1(-2|x + 2|) + 3)) + 2) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\... | -2 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (3(-5(-2|(-3sin(2πx - 1) + 2) + 1|)^2 - 3(-2|(-3sin(2πx - 1) + 2) + 1|)) - 3)/(1(-5(-2|(-3sin(2πx - 1) + 2) + 1|)^2 - 3(-2|(-3sin(2πx - 1) + 2) + 1|)) + 2) in the interval [-10, 10]. Round to the nearest in... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 2|(3(1cos(3π((-3x + 3)/(-1x)) + 1) + 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"
}
] | -5 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 2|(-1cos(2π((-3(1x^2 - 3x + 3) - 2)/(3(1x^2 - 3x + 3) + 3)) + 2) + 2) + 1| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 1 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (2(2|(-2sin(2π(1x^2 + 5x - 5)) + 1) - 2| + 3) - 1)/(-3(2|(-2sin(2π(1x^2 + 5x - 5)) + 1) - 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 |
[
{
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -3|(4(-1sin(1π((-1x - 2)/(1x + 3)) + 1) - 1)^2 + 1(-1sin(1π((-1x - 2)/(1x + 3)) + 1) - 1) + 1) - 3| + 2 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 extremum with the smallest y-value of the function f(x) = 2cos(3π(1(-3|((1x + 2)/(-2x - 2)) - 2| - 1)^2 + 1(-3|((1x + 2)/(-2x - 2)) - 2| - 1) + 5) + 3) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{You... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -2|(-3sin(3π((2(2x^2 + 2x - 2) - 2)/(3(2x^2 + 2x - 2) - 2)) + 1))| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | -2 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (-3(1sin(2π(3|(3x^2 - 2x + 4) - 1|) - 1)) + 3)/(2(1sin(2π(3|(3x^2 - 2x + 4) - 1|) - 1)) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answ... | -10 | MATH |
[
{
"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (2(1sin(3π(3|(-1x^2 + 4x - 2)| - 1) + 3) - 2) + 2)/(1(1sin(3π(3|(-1x^2 + 4x - 2)| - 1) + 3) - 2) + 3) 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 extremum with the largest y-value of the function f(x) = 1|(1((1(2sin(1πx)) - 3)/(-1(2sin(1πx)) - 3))^2 + 1((1(2sin(1πx)) - 3)/(-1(2sin(1πx)) - 3)) + 3) - 2| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\box... | -8 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (-2(-2(3|(2cos(3πx + 3) - 3) - 2| - 2)^2 + 3(3|(2cos(3πx + 3) - 3) - 2| - 2) - 2) + 3)/(-1(-2(3|(2cos(3πx + 3) - 3) - 2| - 2)^2 + 3(3|(2cos(3πx + 3) - 3) - 2| - 2) - 2) - 3) in the interval [-10, 10]. Round to the nearest i... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (-1(-3(1cos(3π(3|x + 2| - 2) - 3) + 1)^2 + 4(1cos(3π(3|x + 2| - 2) - 3) + 1) - 4))/(-3(-3(1cos(3π(3|x + 2| - 2) - 3) + 1)^2 + 4(1cos(3π(3|x + 2| - 2) - 3) + 1) - 4) + 1) in the interval [-10, 10]. Round to ... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1(-1|(3cos(3π((-1x - 3)/(1x + 1))) + 1) + 3| - 2)^2 - 5(-1|(3cos(3π((-1x - 3)/(1x + 1))) + 1) + 3| - 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answe... | -7 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -2sin(2π(2|((-3(-3x^2 - 3x + 5) + 3)/(3(-3x^2 - 3x + 5) + 2)) - 3| - 2) - 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | -3 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = 3(1|((1(-2cos(2πx)))/(1(-2cos(2πx)) + 2)) + 2| - 3)^2 + 1(1|((1(-2cos(2πx)))/(1(-2cos(2πx)) + 2)) + 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 |
[
{
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 3|(5(2sin(2π((3x - 2)/(-2x + 1)) + 3) + 2)^2 + 2(2sin(2π((3x - 2)/(-2x + 1)) + 3) + 2) - 4) + 1| + 1 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 leftmost local maximum of the function f(x) = 3sin(3π(1|((2(1x^2 + 5x - 3))/(-3(1x^2 + 5x - 3) - 2)) + 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": "user"
}
] | -6 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (3(-1sin(3π(-1(-2|x + 1|)^2 + 3(-2|x + 1|) - 2) - 2) + 1) + 2)/(-1(-1sin(3π(-1(-2|x + 1|)^2 + 3(-2|x + 1|) - 2) - 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 average of all x-coordinates of local maxima of the function f(x) = -3|((-3(3sin(3π(-4x^2 - 2x - 2) - 2) + 1) - 1)/(1(3sin(3π(-4x^2 - 2x - 2) - 2) + 1))) - 2| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = (-1(3sin(1π(3|(-1x^2 - 3x - 3) + 3| + 3) - 1)) + 2)/(2(3sin(1π(3|(-1x^2 - 3x - 3) + 3| + 3) - 1)) - 1) 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 leftmost local minimum of the function f(x) = -2|(1sin(3π((-1(-1x^2 + 4x + 3) + 1)/(-1(-1x^2 + 4x + 3) - 2)) + 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"
}... | -2 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 2|(-3((-2(-2sin(3πx + 2)) + 3)/(3(-2sin(3πx + 2)) + 2))^2 + 5((-2(-2sin(3πx + 2)) + 3)/(3(-2sin(3πx + 2)) + 2)) + 3)| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\bo... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -2cos(1π(-4(2|((-3x - 2)/(-3x + 4)) - 1| - 3)^2 - 2(2|((-3x - 2)/(-3x + 4)) - 1| - 3)) - 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 2sin(1π((-2(-3(-2|x - 1|)^2 + 1(-2|x - 1|) + 2) - 3)/(-3(-3(-2|x - 1|)^2 + 1(-2|x - 1|) + 2) - 1))) + 3 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 extremum with the largest y-value of the function f(x) = (2(1sin(2π(-1(-2|x - 3| - 1)^2 + 5(-2|x - 3| - 1) + 2) - 1) - 3) - 2)/(-3(1sin(2π(-1(-2|x - 3| - 1)^2 + 5(-2|x - 3| - 1) + 2) - 1) - 3) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPrese... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 3sin(2π((1(-3|(-4x^2 + 4) + 3| - 1) + 2)/(-3(-3|(-4x^2 + 4) + 3| - 1) + 2)) - 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | -1 | MATH |
[
{
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 3cos(1π(4(1|((-1x - 1)/(-3x - 2)) + 1| - 1)^2 + 4(1|((-1x - 1)/(-3x - 2)) + 1| - 1) + 4) + 3) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | -1 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = (2(3(3cos(3π(3|x + 3| + 1) + 1) + 3)^2 + 3) - 2)/(2(3(3cos(3π(3|x + 3| + 1) + 1) + 3)^2 + 3) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 1cos(1π((-3(-4(-2|x + 3| + 2)^2 - 4(-2|x + 3| + 2) - 3) + 3)/(-3(-4(-2|x + 3| + 2)^2 - 4(-2|x + 3| + 2) - 3) - 3)) - 1) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\b... | -4 | MATH |
[
{
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -2|(-1sin(3π(4((3x + 3)/(-3x))^2 + 5) + 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"
}
] | 1 | MATH |
[
{
"content": "Find the average of all x-coordinates of local minima of the function f(x) = -1cos(3π((1(1(-2|x - 2| + 1)^2 + 2(-2|x - 2| + 1) - 4))/(2(1(-2|x - 2| + 1)^2 + 2(-2|x - 2| + 1) - 4) + 1)) - 1) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{... | 2 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1|(1sin(2π((-3(-3x^2 - 3x - 5))/(3(-3x^2 - 3x - 5) - 2)) + 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"
}
] | -1 | MATH |
[
{
"content": "How many local extrema (both minima and maxima) does the function f(x) = -3sin(1π(4(1|((3x - 3)/(-1x - 2)) - 2| - 2)^2 + 2) - 2) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 222 | MATH |
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