messages listlengths 1 1 | ground_truth stringclasses 45 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (-3(1sin(2π(2|((-2x + 2)/(-3x + 2)) - 1| - 3) - 3) - 3) - 2)/(-2(1sin(2π(2|((-2x + 2)/(-3x + 2)) - 1| - 3) - 3) - 3) + 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 rightmost local extremum of the function f(x) = 4(-1((1(3cos(1πx + 2)) - 3)/(-2(3cos(1πx + 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"
}
] | 9 | MATH |
[
{
"content": "How many local extrema (both minima and maxima) does the function f(x) = -2|(-1(1sin(2π(-2x - 4) + 2) + 3)^2) - 2| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "How many local minima does the function f(x) = 3|(5(-1e^(2(-3x^2 + 2x + 1)) - 2)) - 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 leftmost local extremum of the function f(x) = (-2(-4((-2(-1x^2 - 3x + 3) + 3)/(-3(-1x^2 - 3x + 3) + 4))^2 - 3((-2(-1x^2 - 3x + 3) + 3)/(-3(-1x^2 - 3x + 3) + 4)) + 5) + 3)/(2(-4((-2(-1x^2 - 3x + 3) + 3)/(-3(-1x^2 - 3x + 3) + 4))^2 - 3((-2(-1x^2 - 3x + 3) + 3)/(-3(-1x^2... | -3 | MATH |
[
{
"content": "Find the average of all x-coordinates of local minima of the function f(x) = 1(2(-5(-3x^2 + 3x + 3)^2 + 4(-3x^2 + 3x + 3))^2 - 5(-5(-3x^2 + 3x + 3)^2 + 4(-3x^2 + 3x + 3)) - 4)^2 - 2(2(-5(-3x^2 + 3x + 3)^2 + 4(-3x^2 + 3x + 3))^2 - 5(-5(-3x^2 + 3x + 3)^2 + 4(-3x^2 + 3x + 3)) - 4) - 5 in the interval... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 3(1sin(3π(3(-2|x - 2|)^2 - 3(-2|x - 2|) - 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"
}
] | -10 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = (1(3((-3(-4x^2 - 2x - 2) - 1)/(-3(-4x^2 - 2x - 2) + 1)) - 2) - 2)/(-3(3((-3(-4x^2 - 2x - 2) - 1)/(-3(-4x^2 - 2x - 2) + 1)) - 2) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 5(3sin(3π((-1((-2x)/(-2x - 1)) + 3)/(-3((-2x)/(-2x - 1)))) - 3) - 3)^2 + 3(3sin(3π((-1((-2x)/(-2x - 1)) + 3)/(-3((-2x)/(-2x - 1)))) - 3) - 3) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answ... | 4 | MATH |
[
{
"content": "How many local extrema (both minima and maxima) does the function f(x) = -1((-1(-2cos(2π(3|x| - 3) - 3)) + 3)/(3(-2cos(2π(3|x| - 3) - 3)))) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 121 | MATH |
[
{
"content": "How many local minima does the function f(x) = (1((-3(3(-2|x + 3| + 1)^2 - 5(-2|x + 3| + 1)) - 3)/(1(3(-2|x + 3| + 1)^2 - 5(-2|x + 3| + 1)))) + 3)/(1((-3(3(-2|x + 3| + 1)^2 - 5(-2|x + 3| + 1)) - 3)/(1(3(-2|x + 3| + 1)^2 - 5(-2|x + 3| + 1)))) - 2) have in the interval [-10, 10]?\n\nPresent the answ... | 0 | MATH |
[
{
"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 3(-1(-3|((1x - 1)/(-2x - 1)) + 2| - 1)^2 - 3(-3|((1x - 1)/(-2x - 1)) + 2| - 1) + 2)^2 - 1(-1(-3|((1x - 1)/(-2x - 1)) + 2| - 1)^2 - 3(-3|((1x - 1)/(-2x - 1)) + 2| - 1) + 2) + 4 in the interval [-10, 10]. Round to the near... | -1 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (-1(3(-3e^(-2(-3x - 1)) + 2) - 3) - 1)/(1(3(-3e^(-2(-3x - 1)) + 2) - 3) - 2) 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 x-coordinate of the local maximum of the function f(x) = 4(3(-4((1x + 2)/(-2x - 3)) - 3)^2 - 5(-4((1x + 2)/(-2x - 3)) - 3))^2 + 3(3(-4((1x + 2)/(-2x - 3)) - 3)^2 - 5(-4((1x + 2)/(-2x - 3)) - 3)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex fo... | -1 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -3(3(2sin(1π(-1x^2 + 5x - 2) - 1) + 3)^2 + 1(2sin(1π(-1x^2 + 5x - 2) - 1) + 3) + 4)^2 - 2(3(2sin(1π(-1x^2 + 5x - 2) - 1) + 3)^2 + 1(2sin(1π(-1x^2 + 5x - 2) - 1) + 3) + 4) - 3 in the interval [-10, 10]. Roun... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 2((-3(2sin(1π(-1|x + 2| + 3)) + 3) + 3)/(-1(2sin(1π(-1|x + 2| + 3)) + 3) - 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"... | 10 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 3|(3(-1(-1e^(-2x) + 3)^2 + 5)^2 + 1(-1(-1e^(-2x) + 3)^2 + 5) + 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"
}
] | -1 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -1cos(3π((-2(3(-3|x - 1| + 3)^2 + 5(-3|x - 1| + 3) + 5) - 1)/(-2(3(-3|x - 1| + 3)^2 + 5(-3|x - 1| + 3) + 5) + 3)) - 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in La... | 1 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (1(-3cos(1π(-2(5x^2 - 1x - 2) - 3) - 2)) + 3)/(3(-3cos(1π(-2(5x^2 - 1x - 2) - 3) - 2)) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answe... | -10 | MATH |
[
{
"content": "How many local minima does the function f(x) = -3(-4(2|(-2e^(-1x) + 2) + 3| + 3)^2 + 1(2|(-2e^(-1x) + 2) + 3| + 3) - 2)^2 + 3(-4(2|(-2e^(-1x) + 2) + 3| + 3)^2 + 1(2|(-2e^(-1x) + 2) + 3| + 3) - 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 2|(-1sin(2π(3(5x + 3) + 4) + 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": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 1(-3|(2cos(1π((-2x - 2)/(-2x)) + 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": "Find the x-coordinate of the local extremum of the function f(x) = (2(-1|(2((3x + 3)/(1x)) - 5) + 1| + 3) + 1)/(2(-1|(2((3x + 3)/(1x)) - 5) + 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 minimum with the smallest y-value of the function f(x) = 4(-3(5(-2cos(2πx - 1) + 2) + 1)^2 + 2(5(-2cos(2πx - 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": "... | -9 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 1(3sin(2π((1(-3x^2 - 5x - 1) - 2)/(1(-3x^2 - 5x - 1))) - 1) + 3)^2 - 1(3sin(2π((1(-3x^2 - 5x - 1) - 2)/(1(-3x^2 - 5x - 1))) - 1) + 3) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaT... | -2 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (-2((-3(-3cos(1π((3x + 2)/(-3x + 4)) - 2) + 3) + 1)/(-2(-3cos(1π((3x + 2)/(-3x + 4)) - 2) + 3) - 2)))/(2((-3(-3cos(1π((3x + 2)/(-3x + 4)) - 2) + 3) + 1)/(-2(-3cos(1π((3x + 2)/(-3x + 4)) - 2) + 3) - 2)) - 3) in the interva... | 7 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -3|(-1(3|(4x^2 + 4x - 4) - 3| - 2)^2 - 4(3|(4x^2 + 4x - 4) - 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 rightmost local extremum of the function f(x) = 3(-1cos(3π(3|(-2x) + 1| - 1) + 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 local extremum with the largest y-value of the function f(x) = -1|((-3(2sin(2π(2x + 5)) + 3) - 3)/(-1(2sin(2π(2x + 5)) + 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":... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 3(-2|((-1(1x^2 - 1x - 1) - 2)/(-3(1x^2 - 1x - 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"
}
] | 0 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 2|(-1(-2|((-3x + 3)/(-2x - 1)) + 1| - 2) - 5) - 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 maximum with the smallest y-value of the function f(x) = 1|(2(-3sin(1π(5x + 2) + 1) - 1) + 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": "Find the average of all x-coordinates of local maxima of the function f(x) = -3|(-1(-2sin(1π((1x + 2)/(2x - 3)) + 3) + 1)^2 - 4(-2sin(1π((1x + 2)/(2x - 3)) + 3) + 1) - 2) - 1| + 3 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 local extremum with the largest y-value of the function f(x) = -1cos(1π(2|(-3|((-2x + 1)/(-3x - 2))|) - 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 extrema of the function f(x) = 2|(-2cos(2π(4(-2|x - 3| - 1)^2 + 4(-2|x - 3| - 1) - 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"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = 4(-2(-5(1|x - 1| - 1) - 4)^2 + 5(-5(1|x - 1| - 1) - 4) + 4)^2 - 5(-2(-5(1|x - 1| - 1) - 4)^2 + 5(-5(1|x - 1| - 1) - 4) + 4) + 5 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 with the largest y-value of the function f(x) = 1((-3(2|(-1sin(1πx + 1)) - 3|))/(-1(2|(-1sin(1πx + 1)) - 3|)))^2 + 5((-3(2|(-1sin(1πx + 1)) - 3|))/(-1(2|(-1sin(1πx + 1)) - 3|))) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the a... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -5(-1((3(-3cos(1πx + 2) + 1) - 2)/(2(-3cos(1πx + 2) + 1) - 1)) + 3)^2 + 3(-1((3(-3cos(1πx + 2) + 1) - 2)/(2(-3cos(1πx + 2) + 1) - 1)) + 3) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer ... | 9 | MATH |
[
{
"content": "How many local extrema (both minima and maxima) does the function f(x) = -2cos(2π(-2|((2(2x^2 - 1x + 3) - 1)/(2(2x^2 - 1x + 3)))| + 1) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 2(4(-5(3sin(3πx - 1) + 3)^2 - 1(3sin(3πx - 1) + 3) - 1)^2 + 4(-5(3sin(3πx - 1) + 3)^2 - 1(3sin(3πx - 1) + 3) - 1) + 5)^2 - 3(4(-5(3sin(3πx - 1) + 3)^2 - 1(3sin(3πx - 1) + 3) - 1)^2 + 4(-5(3sin(3πx - 1) + 3... | -9 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 3|(5(1|(3|x + 1| - 1) - 2|)^2 - 4(1|(3|x + 1| - 1) - 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"
... | 0 | MATH |
[
{
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -3(-1|(-5(-3cos(1πx - 1) + 3) - 1) + 1|)^2 - 2(-1|(-5(-3cos(1πx - 1) + 3) - 1) + 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 local maximum with the largest y-value of the function f(x) = 1|(-2sin(2π(2(4x^2 + 5x - 2)^2 + 4(4x^2 + 5x - 2) - 3) + 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": "u... | -5 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 1(-2|((1(2sin(2πx + 2) - 1) - 2)/(2(2sin(2πx + 2) - 1) - 3))| + 1)^2 - 1(-2|((1(2sin(2πx + 2) - 1) - 2)/(2(2sin(2πx + 2) - 1) - 3))| + 1) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPre... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -2|(4(3|(4x^2 + 2x - 1) - 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"
}
] | 1 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -3e^(1(-1|(-5(-1|x - 3|) + 4) - 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"
}
] | 8 | MATH |
[
{
"content": "How many local extrema (both minima and maxima) does the function f(x) = -3(-4((1(3sin(1πx - 1) + 3) + 2)/(3(3sin(1πx - 1) + 3) - 1))^2 + 2((1(3sin(1πx - 1) + 3) + 2)/(3(3sin(1πx - 1) + 3) - 1)) - 4)^2 - 2(-4((1(3sin(1πx - 1) + 3) + 2)/(3(3sin(1πx - 1) + 3) - 1))^2 + 2((1(3sin(1πx - 1) + 3) + 2)/(... | 39 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (-2(-3|(1|(-4x^2 + 5x) - 2| - 1)| - 1) - 3)/(3(-3|(1|(-4x^2 + 5x) - 2| - 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 local minimum with the largest y-value of the function f(x) = (1(-4(-2e^(2((-3x + 3)/(-1x - 2))) - 2)^2 + 3(-2e^(2((-3x + 3)/(-1x - 2))) - 2) - 2) - 2)/(3(-4(-2e^(2((-3x + 3)/(-1x - 2))) - 2)^2 + 3(-2e^(2((-3x + 3)/(-1x - 2))) - 2) - 2) + 3) in the interval [-10, 10]. ... | -4 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 2e^(-2(3|(-3|(2x + 5) + 3|)|)) 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": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (1((2(1sin(3π(-3|x + 2| - 1) + 1) + 1) - 1)/(1(1sin(3π(-3|x + 2| - 1) + 1) + 1))) + 1)/(-2((2(1sin(3π(-3|x + 2| - 1) + 1) + 1) - 1)/(1(1sin(3π(-3|x + 2| - 1) + 1) + 1))) + 3) in the interval [-10, 10]. Round to the nearest... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -3(1cos(3π(2|((-1x + 3)/(2x)) + 3| - 1) - 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"
}
] | -3 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1sin(3π(-1(1|(-1x^2 + 3x - 5) - 1| + 1) + 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 of the function f(x) = (-1(-2(-2|(4x^2 + 3x - 2) - 2|) - 4) + 3)/(1(-2(-2|(4x^2 + 3x - 2) - 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) = (-1(2|(-5(4x^2 + 5x - 1)^2 - 3(4x^2 + 5x - 1) - 1) - 3| - 1) - 1)/(-3(2|(-5(4x^2 + 5x - 1)^2 - 3(4x^2 + 5x - 1) - 1) - 3| - 1) - 2) 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 maximum of the function f(x) = 3e^(2(2|(1(-1x^2 + 2x + 5)^2 + 2(-1x^2 + 2x + 5) + 4) + 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"
}
] | -2 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum of the function f(x) = (-3(-2|(-1(3x + 5) - 5)| + 1) - 3)/(-2(-2|(-1(3x + 5) - 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"
}
] | -3 | MATH |
[
{
"content": "How many local extrema (both minima and maxima) does the function f(x) = 2|(1(2cos(2π(-5x + 2) - 2) - 2) + 3) + 2| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 200 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -4(5(1((-2x)/(-3x + 4))^2 + 4((-2x)/(-3x + 4)) + 1)^2 + 1(1((-2x)/(-3x + 4))^2 + 4((-2x)/(-3x + 4)) + 1) - 1)^2 + 1(5(1((-2x)/(-3x + 4))^2 + 4((-2x)/(-3x + 4)) + 1)^2 + 1(1((-2x)/(-3x + 4))^2 + 4((-2x)/(-3x + 4)) + 1) - 1)... | 1 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum of the function f(x) = -1((-3(4((3x - 3)/(-2x))^2 + 1((3x - 3)/(-2x)) + 3))/(3(4((3x - 3)/(-2x))^2 + 1((3x - 3)/(-2x)) + 3) - 1)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -1e^(-1(-4(5((3x - 1)/(-1x + 2))^2 - 3((3x - 1)/(-1x + 2)) - 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"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 2(-1(4(2sin(3πx + 2) + 2)^2 + 5)^2 + 2(4(2sin(3πx + 2) + 2)^2 + 5) - 4)^2 + 2(-1(4(2sin(3πx + 2) + 2)^2 + 5)^2 + 2(4(2sin(3πx + 2) + 2)^2 + 5) - 4) + 5 in the interval [-10, 10]. Round to the nearest integer... | -9 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 3cos(1π(-4(-1|(2x^2 - 5x - 5) - 3| - 1) + 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"
}
] | -10 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = (-2(-1((-2(1x + 3) - 3)/(-2(1x + 3) + 3))^2 + 3((-2(1x + 3) - 3)/(-2(1x + 3) + 3)) + 5) - 3)/(-2(-1((-2(1x + 3) - 3)/(-2(1x + 3) + 3))^2 + 3((-2(1x + 3) - 3)/(-2(1x + 3) + 3)) + 5) + 3) in the interval [-10, 10]. Round to the neares... | -2 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 5(1|(3|(-1x^2 + 1x + 1) + 1| + 2) + 3| + 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": "How many local extrema (both minima and maxima) does the function f(x) = -3((-1(5(-1|x + 1| + 2)^2 + 4(-1|x + 1| + 2) - 3) - 3)/(1(5(-1|x + 1| + 2)^2 + 4(-1|x + 1| + 2) - 3) + 2))^2 - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 8 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 2|(1|(-3((-1x + 1)/(1x + 3))^2 + 5((-1x + 1)/(1x + 3)) + 5) + 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"
}
] | -1 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = (-3((-3(-2|(1x - 2) + 2| - 2) - 1)/(3(-2|(1x - 2) + 2| - 2) + 3)) + 1)/(3((-3(-2|(1x - 2) + 2| - 2) - 1)/(3(-2|(1x - 2) + 2| - 2) + 3)) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex fo... | 0 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -3(2|(-2e^(-1(4x^2 + 1x - 3)) + 3) - 3| + 1)^2 + 2(2|(-2e^(-1(4x^2 + 1x - 3)) + 3) - 3| + 1) - 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) = (2((3(3(2x - 2)^2 - 2(2x - 2) - 1) + 3)/(-1(3(2x - 2)^2 - 2(2x - 2) - 1) - 1)) + 1)/(2((3(3(2x - 2)^2 - 2(2x - 2) - 1) + 3)/(-1(3(2x - 2)^2 - 2(2x - 2) - 1) - 1)) + 3) in the interval [-10, 10]. Round to th... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 3(1(-2sin(2π(1x - 4) - 1) - 3)^2 - 5(-2sin(2π(1x - 4) - 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"... | -9 | MATH |
[
{
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 2(-2cos(1π(2|(-3|x - 3| + 2) + 1| + 3) - 3) - 1)^2 - 3(-2cos(1π(2|(-3|x - 3| + 2) + 1| + 3) - 3) - 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 x-coordinate of the leftmost local minimum of the function f(x) = 3sin(2π(1(2|(3|x + 2| + 1) - 1| + 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": "user"
}
] | -10 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -1(1cos(1π(-3|((3x)/(1x + 1)) - 2| + 1) + 2) - 2)^2 + 1(1cos(1π(-3|((3x)/(1x + 1)) - 2| + 1) + 2) - 2) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\b... | -4 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = 1(1e^(2(1|((1x - 1)/(-3x + 1)) - 1| + 3)) - 3)^2 + 2(1e^(2(1|((1x - 1)/(-3x + 1)) - 1| + 3)) - 3) - 5 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 local extremum of the function f(x) = -2|(-4(2|(-1x^2 - 2) - 2| + 2)^2 + 4(2|(-1x^2 - 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"
}
] | 0 | MATH |
[
{
"content": "How many local minima does the function f(x) = -5(2|((-2(2x + 5) + 3)/(-2(2x + 5) - 3)) - 3|)^2 - 1(2|((-2(2x + 5) + 3)/(-2(2x + 5) - 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 local extremum with the largest y-value of the function f(x) = (3(-1((-3(3sin(3πx) - 1) + 3)/(2(3sin(3πx) - 1) - 1))) + 3)/(-3(-1((-3(3sin(3πx) - 1) + 3)/(2(3sin(3πx) - 1) - 1))) + 4) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaT... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 3(2|(1(1x + 2)^2 - 3) + 1| + 3)^2 - 1(2|(1(1x + 2)^2 - 3) + 1| + 3) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | -3 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 1(2(5(-1cos(1πx - 3) - 1)^2 - 1(-1cos(1πx - 3) - 1) - 1) + 4)^2 - 3(2(5(-1cos(1πx - 3) - 1)^2 - 1(-1cos(1πx - 3) - 1) - 1) + 4) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the an... | -9 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 5((-1(5(-1e^(-2x) - 3)^2 + 5(-1e^(-2x) - 3) + 1) + 1)/(3(5(-1e^(-2x) - 3)^2 + 5(-1e^(-2x) - 3) + 1) + 2)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your ans... | -8 | MATH |
[
{
"content": "How many local minima does the function f(x) = -3|(-1(1((1x - 2)/(1x))^2 + 5) - 2) + 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 extrema (both minima and maxima) does the function f(x) = -1(3(5(-3cos(3πx + 3) - 1)^2 - 4)^2 + 3(5(-3cos(3πx + 3) - 1)^2 - 4) - 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 3(1cos(3π((3(-3x - 2))/(-3(-3x - 2) - 1)) - 1)) - 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) = 2(-1((3(1cos(2πx + 3)) + 1)/(-3(1cos(2πx + 3)) - 2)) + 2) + 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 average of all x-coordinates of local extrema of the function f(x) = 1|(4((-1(5x + 3) - 2)/(2(5x + 3) - 1))^2 + 3((-1(5x + 3) - 2)/(2(5x + 3) - 1)) - 4) - 2| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | -2 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 4(-1|(-3sin(3π(-5x - 4) + 3) + 1) - 2| - 2)^2 + 1(-1|(-3sin(3π(-5x - 4) + 3) + 1) - 2| - 2) + 4 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 maximum of the function f(x) = -2|((-3(-1|(3x^2 + 2x + 2)| - 3))/(1(-1|(3x^2 + 2x + 2)| - 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"
}
] | -9 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (3(-1|(-3|(-1cos(3πx - 3) + 3)| - 2) - 2| - 1))/(-1(-1|(-3|(-1cos(3πx - 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}",
... | -9 | MATH |
[
{
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -3|(2cos(3π(-1((1x)/(3x + 1)) + 4) - 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"
}
] | -1 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -2|(3(-3((1x - 3)/(-3x - 3))^2 + 2) + 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"
}
] | 3 | MATH |
[
{
"content": "How many local minima does the function f(x) = (-3(1|(3(4x)^2 + 3(4x) + 3)| + 3) - 1)/(-1(1|(3(4x)^2 + 3(4x) + 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 local maximum of the function f(x) = -5((3(-1|(4x + 2) - 2| + 3) + 1)/(1(-1|(4x + 2) - 2| + 3) - 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 average of all x-coordinates of local extrema of the function f(x) = 1(-1e^(1((-3(-3|x - 1| + 2) - 2)/(-3(-3|x - 1| + 2)))) - 2)^2 - 2(-1e^(1((-3(-3|x - 1| + 2) - 2)/(-3(-3|x - 1| + 2)))) - 2) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex form... | 1 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = 2|(-1(1|(-2x^2 - 2x - 1) + 1| - 2)^2 - 1(1|(-2x^2 - 2x - 1) + 1| - 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) = -5((2(5(-1sin(2πx - 1) - 1)^2 - 5(-1sin(2πx - 1) - 1) - 4) + 1)/(-2(5(-1sin(2πx - 1) - 1)^2 - 5(-1sin(2πx - 1) - 1) - 4) + 1))^2 - 3((2(5(-1sin(2πx - 1) - 1)^2 - 5(-1sin(2πx - 1) - 1) - 4) + 1)/(-2(5(-1sin(2πx - 1) - 1)^2 -... | -9 | MATH |
[
{
"content": "How many local minima does the function f(x) = -1(1|(-4(-3e^(1x) + 2)^2 - 3(-3e^(1x) + 2) - 3) + 2| - 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 minima does the function f(x) = -5(-3e^(2(-2((3x + 1)/(-2x + 3))^2 + 4((3x + 1)/(-2x + 3)) + 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) = 3|((3(-4(3|x|)^2 + 5(3|x|) + 5) + 1)/(-2(-4(3|x|)^2 + 5(3|x|) + 5) + 3)) + 1| - 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) = 1|(2|(-1(-5x - 5)^2 + 2(-5x - 5) + 5) - 1|)| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.