messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the total number of local minima and maxima for f(x) = 2|(3sin(2π(5x^2 + 5x + 1) + 3) + 1) + 3| + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 502 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = (3(-1sin(1π(1x^2 + 3x - 2) + 2) + 3) - 1)/(2(-1sin(1π(1x^2 + 3x - 2) + 2) + 3) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 104 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -5(1|(-2sin(2π((1x - 2)/(-3x - 3)) + 2) - 1) + 1| - 2)^2 - 2(1|(-2sin(2π((1x - 2)/(-3x - 3)) + 2) - 1) + 1| - 2) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 51 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 2cos(1π(3(1|(-2x - 3) + 2| + 1)^2 + 4(1|(-2x - 3) + 2| + 1) + 1) - 2) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 267 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = (1(1(1cos(1πx + 1) + 1) + 3) + 2)/(2(1(1cos(1πx + 1) + 1) + 3) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many local minima does the function f(x) = 1sin(1π(2|(3x - 2) + 2| + 2) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -2((-3(-2cos(1πx + 3)) - 1)/(-2(-2cos(1πx + 3)) + 3)) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = (1(1sin(1π(3x^2 - 1x - 2) + 3) + 1) + 3)/(-1(1sin(1π(3x^2 - 1x - 2) + 3) + 1) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 567 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -2|(2sin(1π(-1x + 3) + 1) - 3)| + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = (-3(1sin(2π(-5(-2|x + 1| - 1) - 1) - 3) + 3) + 3)/(-2(1sin(2π(-5(-2|x + 1| - 1) - 1) - 3) + 3) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 194 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -2|(-4(1cos(1πx)) - 5) - 2| + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "How many local minima does the function f(x) = -5(1|(-1sin(1πx) + 2) + 2| - 3)^2 - 1(1|(-1sin(1πx) + 2) + 2| - 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3|(-1cos(1π(1(-3x + 5)^2 + 1(-3x + 5) - 5) - 3) - 1) + 1| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 494 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 4((-1(-3cos(3π(-3x^2 - 4)) + 3) - 2)/(3(-3cos(3π(-3x^2 - 4)) + 3) - 2)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 537 | MATH |
[
{
"content": "How many local minima does the function f(x) = 2|(1(-1cos(1π((2x - 1)/(1x)) + 1) - 2)^2 - 3(-1cos(1π((2x - 1)/(1x)) + 1) - 2) + 4) + 2| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3cos(2π(1|((2x)/(-2x - 1)) + 2|) + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -1(-2e^(1(4x - 1)) + 1)^2 + 2(-2e^(1(4x - 1)) + 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = (-2(2cos(1π(2|x|) + 3)) + 1)/(-1(2cos(1π(2|x|) + 3)) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "How many local minima does the function f(x) = -3sin(1π((-3(1x + 2) + 3)/(-2(1x + 2))) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (-3(1(2e^(-2x) - 3)^2 + 1(2e^(-2x) - 3) - 2) - 2)/(-3(1(2e^(-2x) - 3)^2 + 1(2e^(-2x) - 3) - 2) + 4) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -2cos(3π(-2|((1x)/(2x + 1)) - 1| - 1) - 1) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = -2cos(2π(5(-2|(-1x^2 - 5x + 1) + 1| + 2) + 3) - 1) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 244 | MATH |
[
{
"content": "How many local minima does the function f(x) = 1cos(3π(-3(-4(1|x - 3| + 1)^2 - 1(1|x - 3| + 1) - 5) + 2) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 243 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 1|(-3sin(2π(-4((-2x + 2)/(-1x + 2))^2 + 3((-2x + 2)/(-1x + 2))) - 1) + 1) - 2| + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 153 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3(1cos(2π(1|x + 3| + 2) + 2) + 2)^2 - 2(1cos(2π(1|x + 3| + 2) + 2) + 2) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -2cos(1π(4(-1((-3x - 3)/(-2x))^2 + 1((-3x - 3)/(-2x)) - 2) + 5) + 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -2sin(1π(-3((-2x - 3)/(-3x - 3))^2 + 1((-2x - 3)/(-3x - 3))) - 1) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = (1(1|(4(-2cos(1πx - 3)) + 5) + 2| + 2) + 2)/(1(1|(4(-2cos(1πx - 3)) + 5) + 2| + 2) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 1|(-2cos(3π(4x^2 + 5x - 5) + 3) + 1) - 2| + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 497 | MATH |
[
{
"content": "How many local minima does the function f(x) = -3(2cos(1π((1x - 1)/(1x - 2)) - 3))^2 - 2(2cos(1π((1x - 1)/(1x - 2)) - 3)) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = (2(-2sin(2π(-1x^2 - 1x + 2) + 2) - 1))/(2(-2sin(2π(-1x^2 - 1x + 2) + 2) - 1) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 236 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 2cos(2π(5((-3x - 1)/(-1x + 2))^2 - 5((-3x - 1)/(-1x + 2)) + 3) - 1) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 127 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = (2(-2sin(1π(2x^2 - 3x - 5) + 3)) - 3)/(-1(-2sin(1π(2x^2 - 3x - 5) + 3)) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 294 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -1|(1(-2cos(3π(1x + 2) - 2) - 2)^2 + 3(-2cos(3π(1x + 2) - 2) - 2) - 2) + 1| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 173 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 5(-4(-1sin(2π((1x + 1)/(3x)) - 2) - 1)^2 + 4(-1sin(2π((1x + 1)/(3x)) - 2) - 1) - 5) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1|(3((2(1cos(2πx - 3) + 1) + 1)/(1(1cos(2πx - 3) + 1) - 3))^2 + 3((2(1cos(2πx - 3) + 1) + 1)/(1(1cos(2πx - 3) + 1) - 3)) + 3) - 1| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your an... | 80 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5(-3sin(1π((2x - 1)/(-3x)) + 3) + 3)^2 - 4(-3sin(1π((2x - 1)/(-3x)) + 3) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -1(3cos(3π((-3x - 1)/(-3x)) + 3) + 1)^2 - 3(3cos(3π((-3x - 1)/(-3x)) + 3) + 1) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -3sin(1π(5(-3((-1x + 1)/(-2x - 3)) + 2)^2 - 3(-3((-1x + 1)/(-2x - 3)) + 2) - 4)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 66 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = 3cos(3π((-1(2(2|x + 2| - 2)^2 + 1(2|x + 2| - 2) - 4) - 3)/(-2(2(2|x + 2| - 2)^2 + 1(2|x + 2| - 2) - 4) + 3)) + 2) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -3cos(3π((1(-3|x + 2| + 3) - 2)/(-1(-3|x + 2| + 3) - 2))) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -3sin(2π((1(-1x - 3) + 2)/(2(-1x - 3) - 1)) - 2) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 1cos(3π(2|(3x - 2) - 1| - 2) + 3) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = (2(-2cos(2π(2|(2x^2 - 4x + 2) - 3| + 1) + 2) - 2) + 2)/(-3(-2cos(2π(2|(2x^2 - 4x + 2) - 3| + 1) + 2) - 2) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 440 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1cos(3π((-3(-1x^2 + 3x - 3) - 3)/(3(-1x^2 + 3x - 3) + 1)) - 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1|((1(3sin(1π(2x^2 - 4) - 3) + 3) - 1)/(-1(3sin(1π(2x^2 - 4) - 3) + 3) - 1)) + 1| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 401 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 1|(-1((-2(3sin(1πx + 3) + 1) + 3)/(-2(3sin(1πx + 3) + 1)))^2 - 1((-2(3sin(1πx + 3) + 1) + 3)/(-2(3sin(1πx + 3) + 1))) - 5) + 3| - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -1(1|(3e^(-1(4x + 5))) - 1| - 2)^2 - 3(1|(3e^(-1(4x + 5))) - 1| - 2) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 2sin(2π(-1|(5x^2 - 5x + 1) - 3| + 3) + 3) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 507 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 3(-3|(4(-1sin(1πx + 1) + 2) + 2) - 1| - 2)^2 - 5(-3|(4(-1sin(1πx + 1) + 2) + 2) - 1| - 2) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many local minima does the function f(x) = (-2(-2|(2e^(-2(1x - 5))) + 1| - 3))/(3(-2|(2e^(-2(1x - 5))) + 1| - 3) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = (1(1|(2cos(3π(-2x + 5) - 1) + 2) - 3| - 3))/(3(1|(2cos(3π(-2x + 5) - 1) + 2) - 3| - 3) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 4((3(1cos(1π(1|x - 3| - 1) + 2) + 2) + 2)/(3(1cos(1π(1|x - 3| - 1) + 2) + 2) + 1))^2 + 3((3(1cos(1π(1|x - 3| - 1) + 2) + 2) + 2)/(3(1cos(1π(1|x - 3| - 1) + 2) + 2) + 1)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Y... | 21 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-3(1(2sin(1π(1|x - 2| + 1)))) + 1)/(3(1(2sin(1π(1|x - 2| + 1))))) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = 1sin(3π(-4(-3(-3|x - 3| + 1))^2 + 2(-3(-3|x - 3| + 1)) - 5) + 3) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 126 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = (-1(-1|(-2sin(1π(1x - 4) - 1) - 1) - 1| + 3) + 3)/(-1(-1|(-2sin(1π(1x - 4) - 1) - 1) - 1| + 3)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = (2(-3|(2sin(2πx - 2)) + 1| - 3))/(3(-3|(2sin(2πx - 2)) + 1| - 3)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = (-1(-1cos(2π(2(1|x + 1| + 3) - 2) - 3) + 3) + 2)/(-2(-1cos(2π(2(1|x + 1| + 3) - 2) - 3) + 3) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many local minima does the function f(x) = 1cos(2π(-3|(1(-1x - 4)^2 - 3(-1x - 4) + 5) + 2|)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 264 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (3(2cos(1π(5x + 2) - 2) + 3) - 1)/(1(2cos(1π(5x + 2) - 2) + 3) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 52 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = (-1(-3cos(3π(-5x^2 - 3x - 4) + 3)))/(3(-3cos(3π(-5x^2 - 3x - 4) + 3)) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 242 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -1cos(2π(3((-2x)/(-3x + 1)) + 3) - 3) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -2(-3|(-1sin(2π((-1x - 2)/(1x)))) - 2| - 1)^2 - 2(-3|(-1sin(2π((-1x - 2)/(1x)))) - 2| - 1) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -3|(-2(-3e^(1(-1x^2 + 5x + 1)) - 3) + 5) + 2| where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = (-2(4(2sin(1πx + 3) - 2) - 5) + 2)/(-3(4(2sin(1πx + 3) - 2) - 5) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 5(-3sin(1π((-1(-3|x - 2| + 3) - 3)/(-2(-3|x - 2| + 3) + 3)) + 2) + 3)^2 + 2(-3sin(1π((-1(-3|x - 2| + 3) - 3)/(-2(-3|x - 2| + 3) + 3)) + 2) + 3) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\... | 38 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -3cos(1π(4(-2|(1x^2 + 3x + 3) + 3| + 3) - 3) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 251 | MATH |
[
{
"content": "How many local minima does the function f(x) = -2cos(3π((2(2|(1x^2 + 3x) - 3| + 1) + 1)/(-1(2|(1x^2 + 3x) - 3| + 1) - 2)) - 3) - 3 have in the interval [-10, 10]?\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|(-5(1(1sin(1πx - 1) - 3) + 5)^2 - 3(1(1sin(1πx - 1) - 3) + 5) - 4) + 1| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = -3(3|(-3sin(1πx + 1) + 3) - 2| + 3)^2 - 2(3|(-3sin(1πx + 1) + 3) - 2| + 3) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 2sin(1π(-5(1|x + 1| - 2) + 5) + 1) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 101 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -2((-2(-2sin(2πx) - 1) - 1)/(2(-2sin(2πx) - 1) + 3)) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 3|(3sin(2π(1x - 2) + 1) + 3) + 3| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 1(3|(5((-1x)/(3x)) + 1) + 3| + 1)^2 + 4(3|(5((-1x)/(3x)) + 1) + 3| + 1) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "How many local minima does the function f(x) = -5(-2sin(3π(-1|(5x^2 + 2x - 5) - 3| - 1) + 3) - 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 256 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = -1(2((3(-2cos(2πx - 3) + 2) - 1)/(-2(-2cos(2πx - 3) + 2) - 3)) - 2)^2 + 5(2((3(-2cos(2πx - 3) + 2) - 1)/(-2(-2cos(2πx - 3) + 2) - 3)) - 2) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 20 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -1cos(1π(-5((-2(-1|x - 2| - 1) - 3)/(-1(-1|x - 2| - 1))) - 3) + 2) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -1cos(1π(-2|(-3x - 2)| - 3) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -2sin(1π(2((3x + 2)/(-3x - 1)) - 2) - 2) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -1|(-1(3(-3sin(2πx + 2) - 1)^2 + 4(-3sin(2πx + 2) - 1) + 3) - 3) - 2| + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = (2(1(-3cos(2πx - 3) + 1)^2 - 5(-3cos(2πx - 3) + 1) + 5) + 3)/(1(1(-3cos(2πx - 3) + 1)^2 - 5(-3cos(2πx - 3) + 1) + 5) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 80 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = (-1(-5(-1|(1cos(3πx + 2)) + 2| + 1)^2 + 3(-1|(1cos(3πx + 2)) + 2| + 1) - 3) - 1)/(-3(-5(-1|(1cos(3πx + 2)) + 2| + 1)^2 + 3(-1|(1cos(3πx + 2)) + 2| + 1) - 3) + 4) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 30 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (3(-4(2cos(2π(3|x - 1| - 2) + 3) - 1)^2 - 5(2cos(2π(3|x - 1| - 2) + 3) - 1)) - 1)/(-2(-4(2cos(2π(3|x - 1| - 2) + 3) - 1)^2 - 5(2cos(2π(3|x - 1| - 2) + 3) - 1)) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your an... | 119 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -1(1|((-2(-2x - 5))/(-3(-2x - 5)))| + 1)^2 - 4(1|((-2(-2x - 5))/(-3(-2x - 5)))| + 1) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 46 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = 2((-1(3cos(1π(1|x - 1| + 1) - 1) + 3) + 1)/(2(3cos(1π(1|x - 1| + 1) - 1) + 3) - 1)) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 2cos(1π(-1((-1x + 1)/(3x))^2 + 5((-1x + 1)/(3x)) + 1)) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = (-1(-2sin(2π(1x^2 - 1x - 1) - 2) + 1))/(3(-2sin(2π(1x^2 - 1x - 1) - 2) + 1) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 201 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1|((2(-1e^(-1(-5x - 3)) - 3) - 2)/(3(-1e^(-1(-5x - 3)) - 3))) - 1| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 54 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = 2|(1((-1(1sin(2πx + 1) + 1))/(2(1sin(2πx + 1) + 1) - 1)) + 2) + 2| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -2sin(1π(1|((-2(-2x^2 + 5x - 1))/(-3(-2x^2 + 5x - 1) + 1)) - 3| - 2)) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -1((3(-4(1sin(2πx - 1) + 3) - 4) - 1)/(-2(-4(1sin(2πx - 1) + 3) - 4) - 3))^2 - 2((3(-4(1sin(2πx - 1) + 3) - 4) - 1)/(-2(-4(1sin(2πx - 1) + 3) - 4) - 3)) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your an... | 20 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 3(-1cos(3π(1x - 3) - 3))^2 + 4(-1cos(3π(1x - 3) - 3)) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 2|(5(-2sin(3π(1x + 4) + 1) - 3)^2 + 5(-2sin(3π(1x + 4) + 1) - 3) - 5) - 1| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -2sin(1π((-1(3|(3x^2 + 1x - 3) + 2| - 1) - 2)/(1(3|(3x^2 + 1x - 3) + 2| - 1))) + 2) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2sin(1π(1|((2x - 1)/(-2x - 1)) - 2| - 2) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (-3(-3(2cos(2π(1|x| + 3) - 3) - 2)) + 3)/(-1(-3(2cos(2π(1|x| + 3) - 3) - 2)) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 1sin(1π(1(2|((-3x + 1)/(-1x)) + 3| - 1)) + 2) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 4(-1|(-3cos(3πx) + 1) + 2| - 2)^2 + 4(-1|(-3cos(3πx) + 1) + 2| - 2) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 5((-3(1sin(3πx + 3) + 2) + 1)/(-2(1sin(3πx + 3) + 2) - 1)) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -2sin(2π(-3|(-1x - 5) + 1| - 3)) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
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