messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = -1(5(1|x + 3|)^2 + 5(1|x + 3|) + 5) - 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) = 1cos(1π(1(-3|x - 2| - 2)^2 - 5(-3|x - 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"
}
] | -10 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -1cos(2π((-3(-1(-2x + 3)^2 + 4(-2x + 3)) + 1)/(1(-1(-2x + 3)^2 + 4(-2x + 3)))) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | -1 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -2sin(3π(-1(3(3|((-3x + 3)/(-3x - 1)) + 2| - 2)^2 - 3) + 5) + 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 3cos(2π((3(1(1|(-3x - 3) + 3| - 3)^2 + 2(1|(-3x - 3) + 3| - 3) + 4) + 2)/(1(1(1|(-3x - 3) + 3| - 3)^2 + 2(1|(-3x - 3) + 3| - 3) + 4) + 2)) + 1) + 3 in the interval [-10, 10]. Round to the nearest integer.\... | -1 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 1((-2(2|x - 1| - 1) + 2)/(-2(2|x - 1| - 1)))^2 - 4((-2(2|x - 1| - 1) + 2)/(-2(2|x - 1| - 1))) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your... | 1 | MATH |
[
{
"content": "How many local extrema (both minima and maxima) does the function f(x) = (3(-1|(1e^(-2(-3x^2 - 2x + 4)) - 1) - 2| + 3) - 1)/(-1(-1|(1e^(-2(-3x^2 - 2x + 4)) - 1) - 2| + 3) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 53 | MATH |
[
{
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -1cos(3π((-2(-5x + 2) - 2)/(-1(-5x + 2) - 2)) + 2) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "How many local extrema (both minima and maxima) does the function f(x) = 3e^(-1(-5(4x^2 + 4x + 2) + 5)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = (1(-1(-2|x + 1| + 1)^2 + 2(-2|x + 1| + 1) + 5) + 1)/(-1(-1(-2|x + 1| + 1)^2 + 2(-2|x + 1| + 1) + 5) + 3) 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 x-coordinate of the rightmost local minimum of the function f(x) = -2|(4((-2x - 2)/(1x + 2))^2 - 4((-2x - 2)/(1x + 2)) - 5) - 3| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -2|(-1(-1(-2e^(-2x) + 3)^2 - 4(-2e^(-2x) + 3) + 2) + 1) - 2| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = (-1(3e^(2(-1|(5x + 3)| - 1)) - 2) + 1)/(-3(3e^(2(-1|(5x + 3)| - 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"
}
] | 2 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (1(2|(-5(5x - 2)^2 + 4(5x - 2))|) - 1)/(-2(2|(-5(5x - 2)^2 + 4(5x - 2))|) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 0 | MATH |
[
{
"content": "How many local extrema (both minima and maxima) does the function f(x) = 2((1(4(-2|(2sin(3πx - 3) + 2) + 3| + 3) + 5) + 2)/(-3(4(-2|(2sin(3πx - 3) + 2) + 3| + 3) + 5) + 4))^2 - 2((1(4(-2|(2sin(3πx - 3) + 2) + 3| + 3) + 5) + 2)/(-3(4(-2|(2sin(3πx - 3) + 2) + 3| + 3) + 5) + 4)) - 5 have in the inter... | 60 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (3(5(1x^2 - 2x - 3) + 5) - 2)/(1(5(1x^2 - 2x - 3) + 5) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -2|(-2sin(1π(1(-3((2x + 1)/(-1x - 1)) - 1)^2 + 4(-3((2x + 1)/(-1x - 1)) - 1) + 1) - 2) - 2) + 2| + 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) = -2|(1cos(1π(-1(-4((-2x + 3)/(2x - 1))^2 + 4((-2x + 3)/(2x - 1)) - 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}",
"role": "... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1(3cos(1π(3(-2|((3x + 3)/(3x + 2)) + 2| + 1)^2 + 3(-2|((3x + 3)/(3x + 2)) + 2| + 1) - 5) + 3) + 2) - 4 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 local extremum with the smallest y-value of the function f(x) = (-2(3|(3(-1x - 5)^2 + 5(-1x - 5) - 5) - 2| - 2) - 3)/(-3(3|(3(-1x - 5)^2 + 5(-1x - 5) - 5) - 2| - 2) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\b... | -6 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 2((-1(1sin(2π(3(-3|x - 2| + 2)^2 - 2(-3|x - 2| + 2) + 4) + 3)))/(-1(1sin(2π(3(-3|x - 2| + 2)^2 - 2(-3|x - 2| + 2) + 4) + 3)) - 3)) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the ... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -2|((2(-2(5x^2 - 2x - 1) + 5) + 1)/(1(-2(5x^2 - 2x - 1) + 5) - 3)) + 1| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 0 | MATH |
[
{
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -5(-4(2e^(1(-3|x - 1|)) - 2)^2 + 4(2e^(1(-3|x - 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"
}
] | -9 | MATH |
[
{
"content": "Find the average of all x-coordinates of local minima of the function f(x) = 1|((3(3(-1x^2 - 5x + 5) + 2) + 1)/(2(3(-1x^2 - 5x + 5) + 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 maximum with the largest y-value of the function f(x) = (-1(1(-2(-2|x + 1| + 3) + 2)^2 + 3(-2(-2|x + 1| + 3) + 2) + 1) + 1)/(1(1(-2(-2|x + 1| + 3) + 2)^2 + 3(-2(-2|x + 1| + 3) + 2) + 1)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answ... | -2 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 1|(-1(1cos(2π(-4x^2 + 4x + 5) - 3) + 3) - 4) + 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 rightmost local extremum of the function f(x) = (2(-3cos(3π(3(-1(1|x - 1| - 1) - 1)^2 - 1(-1(1|x - 1| - 1) - 1) + 4)) - 2) + 3)/(2(-3cos(3π(3(-1(1|x - 1| - 1) - 1)^2 - 1(-1(1|x - 1| - 1) - 1) + 4)) - 2) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nP... | 10 | MATH |
[
{
"content": "How many local minima does the function f(x) = -1((-3(-2x + 3) + 1)/(1(-2x + 3) + 2))^2 + 4((-3(-2x + 3) + 1)/(1(-2x + 3) + 2)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -1((-2(1(1sin(2πx + 3)) - 2) - 3)/(-3(1(1sin(2πx + 3)) - 2) + 4))^2 + 1((-2(1(1sin(2πx + 3)) - 2) - 3)/(-3(1(1sin(2πx + 3)) - 2) + 4)) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in ... | 0 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 2|(-1(-1((3x + 1)/(-2x - 2)) - 3)^2 - 2) - 2| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = 4(2((2x - 3)/(1x))^2 + 3) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many local minima does the function f(x) = -5(2|((1(1x^2 - 4x - 1) - 1)/(1(1x^2 - 4x - 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": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -1(3sin(2π((3(-4x - 3) + 2)/(2(-4x - 3))) - 3) - 3)^2 - 4(3sin(2π((3(-4x - 3) + 2)/(2(-4x - 3))) - 3) - 3) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format:... | -1 | MATH |
[
{
"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 2e^(-1(1(-2(2|((-3x - 1)/(-1x + 2))| - 2))^2)) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = 2(-1|(-4((-3x + 3)/(3x + 3))^2 + 4((-3x + 3)/(3x + 3)) - 1) - 1| + 1) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 5(2|((2x - 2)/(-1x)) - 1|)^2 + 2(2|((2x - 2)/(-1x)) - 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 of the function f(x) = 3|(2e^(-2((-2x - 3)/(-1x - 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"
}
] | -2 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum of the function f(x) = (-2(1|(-4x + 1) - 2| + 1) + 2)/(-3(1|(-4x + 1) - 2| + 1) + 4) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = 2e^(1(1((-2x)/(1x + 1)) - 5)) - 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 of the function f(x) = 2((-1(-2|(-1x^2 - 2x - 1) + 1| + 3) - 1)/(1(-2|(-1x^2 - 2x - 1) + 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"
}
] | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local extremum of the function f(x) = -1|(1((-2x + 3)/(1x)) + 4)| - 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) = -2((1(2sin(3π(5x^2 - 1x) - 3) + 1) - 3)/(-2(2sin(3π(5x^2 - 1x) - 3) + 1) + 3)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 492 | MATH |
[
{
"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 1|((-3(-3x^2 - 5x - 1) + 3)/(3(-3x^2 - 5x - 1) + 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 with the smallest y-value of the function f(x) = (-1(3(-3|(4(1cos(3πx + 2) - 3) + 1) + 1| - 3)^2 + 5(-3|(4(1cos(3πx + 2) - 3) + 1) + 1| - 3) + 2) + 3)/(1(3(-3|(4(1cos(3πx + 2) - 3) + 1) + 1| - 3)^2 + 5(-3|(4(1cos(3πx + 2) - 3) + 1) + 1| - 3) + 2)) in the... | -10 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -1|((-3(-3(-5x^2 + 2x + 3) - 3) + 1)/(3(-3(-5x^2 + 2x + 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": "... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -3e^(2((-1(4(-2|x + 2|)^2 + 5(-2|x + 2|) - 5) + 2)/(2(4(-2|x + 2|)^2 + 5(-2|x + 2|) - 5)))) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | -3 | MATH |
[
{
"content": "Find the average of all x-coordinates of local minima of the function f(x) = (-1(2|(1(-4x - 1)^2 + 1(-4x - 1) + 3) - 3| - 1) + 1)/(-2(2|(1(-4x - 1)^2 + 1(-4x - 1) + 3) - 3| - 1) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 0 | MATH |
[
{
"content": "Find the x-coordinate of the local minimum of the function f(x) = (1(-2(-1|(4x^2 - 3x + 5) + 3| + 2) + 2) - 1)/(-2(-2(-1|(4x^2 - 3x + 5) + 3| + 2) + 2) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 0 | MATH |
[
{
"content": "How many local minima does the function f(x) = (-2(3e^(-1(2|x - 3|)) - 3) + 3)/(-2(3e^(-1(2|x - 3|)) - 3) - 1) 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) = 2sin(3π(2|(-3((-3x + 1)/(-3x - 1))^2 - 4((-3x + 1)/(-3x - 1)) - 5) - 3| + 3) - 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 0 | MATH |
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