messages listlengths 1 1 | ground_truth stringclasses 194 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2cos(1π(-3(5(3|x - 1| + 2) - 1)^2 + 5(5(3|x - 1| + 2) - 1) - 5) + 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 276 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = -2cos(3π(-4(-1|x + 1| - 2)^2 + 4(-1|x + 1| - 2)) + 1) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 234 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -3sin(3π(-4x - 3) - 1) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = (-2(2sin(3π(-2|x| + 1) + 2) - 1) + 3)/(-2(2sin(3π(-2|x| + 1) + 2) - 1) + 1) 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) = (1(3cos(1π(-4(-2x - 5)^2 - 2(-2x - 5) - 5) + 2) - 1) - 2)/(-2(3cos(1π(-4(-2x - 5)^2 - 2(-2x - 5) - 5) + 2) - 1) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 494 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -1(-2cos(1π(-3|x + 1|) - 3)) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = (-1(2(2|(-5x + 2) + 3|)^2 - 3(2|(-5x + 2) + 3|) + 4) + 2)/(3(2(2|(-5x + 2) + 3|)^2 - 3(2|(-5x + 2) + 3|) + 4) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 3(3|x + 1|)^2 - 1(3|x + 1|) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5((2(-2|x - 3| + 3) + 3)/(1(-2|x - 3| + 3)))^2 - 2((2(-2|x - 3| + 3) + 3)/(1(-2|x - 3| + 3))) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = (-3(-2sin(3πx - 1) - 3) - 3)/(3(-2sin(3πx - 1) - 3) - 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) = (-2(3cos(1π(-1x^2 - 4x + 1) - 2) - 1) + 1)/(3(3cos(1π(-1x^2 - 4x + 1) - 2) - 1) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 209 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = (-2(-2cos(2π(2|(1x^2 - 4x - 2) + 3| + 2) - 3) + 1) + 3)/(-1(-2cos(2π(2|(1x^2 - 4x - 2) + 3| + 2) - 3) + 1) + 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 543 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -2(3sin(1π(4x^2 - 2x + 4) + 1) - 3) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 575 | MATH |
[
{
"content": "How many local minima does the function f(x) = -2sin(2π(-4(-2|((2x + 1)/(1x - 3)) + 3| - 2)^2 - 3(-2|((2x + 1)/(1x - 3)) + 3| - 2) + 3) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 235 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 1(-5((-1(-1cos(2πx - 2) + 1) + 3)/(-2(-1cos(2πx - 2) + 1)))^2 - 4((-1(-1cos(2πx - 2) + 1) + 3)/(-2(-1cos(2πx - 2) + 1))) - 4) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 79 | MATH |
[
{
"content": "How many local minima does the function f(x) = 1sin(1π(5x^2 + 5x - 4) + 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 251 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = -3|((-3(3x^2 + 3x - 2) - 2)/(2(3x^2 + 3x - 2) - 1)) - 2| + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -4(-2|((-3(-2cos(3πx + 3) - 1) - 2)/(1(-2cos(3πx + 3) - 1) + 3)) + 3| + 3)^2 - 1(-2|((-3(-2cos(3πx + 3) - 1) - 2)/(1(-2cos(3πx + 3) - 1) + 3)) + 3| + 3) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 56 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 1e^(1((-3x - 3)/(-3x + 1))) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -2cos(2π((3(1x^2 - 5) - 3)/(-1(1x^2 - 5) + 2)) - 3) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 3|((2(-2sin(3πx - 2)) - 1)/(-1(-2sin(3πx - 2)) - 1)) + 3| + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 119 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = (-1(-1(3(1cos(2πx - 1) + 3))^2 + 1(3(1cos(2πx - 1) + 3)) - 5) - 2)/(-1(-1(3(1cos(2πx - 1) + 3))^2 + 1(3(1cos(2πx - 1) + 3)) - 5) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 40 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = (1(5(-3(1|x - 1| - 2))^2 + 1(-3(1|x - 1| - 2)) + 4) + 2)/(2(5(-3(1|x - 1| - 2))^2 + 1(-3(1|x - 1| - 2)) + 4) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = (3(-1|(-2sin(1πx - 2) + 3) + 1| - 1) + 1)/(3(-1|(-2sin(1πx - 2) + 3) + 1| - 1) - 2) 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|(3(2sin(1π(-4x^2 + 3x + 5) + 1) - 1) - 2) - 3| - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 290 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 1(-1(3sin(1πx + 1)) - 2)^2 - 3(-1(3sin(1πx + 1)) - 2) - 1 where -10 ≤ x ≤ 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) = -1(-3cos(1πx + 3)) + 1 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 minima for the function f(x) = -3|(1cos(2π(1(2x^2 - 2x + 5) - 3) - 3) - 3) + 1| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 290 | MATH |
[
{
"content": "How many local minima does the function f(x) = 3sin(2π(4x^2 - 5x + 5)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 257 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = (3(-3sin(1π(1x - 1) - 1) + 1) + 1)/(2(-3sin(1π(1x - 1) - 1) + 1) + 1) where -10 ≤ x ≤ 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((-2(3cos(2π(-2x - 5) - 2) + 2) + 2)/(3(3cos(2π(-2x - 5) - 2) + 2) - 1))^2 + 1((-2(3cos(2π(-2x - 5) - 2) + 2) + 2)/(3(3cos(2π(-2x - 5) - 2) + 2) - 1)) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex fo... | 239 | MATH |
[
{
"content": "How many local minima does the function f(x) = 2(2sin(3π((-1x + 3)/(-2x + 3)) - 3) - 3)^2 - 1(2sin(3π((-1x + 3)/(-2x + 3)) - 3) - 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = (2(3(-1(3|x + 3| + 1) + 1)^2 + 1(-1(3|x + 3| + 1) + 1) - 3))/(-2(3(-1(3|x + 3| + 1) + 1)^2 + 1(-1(3|x + 3| + 1) + 1) - 3) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 3 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 5(-2sin(1π(-2|x - 2|) + 3)) - 2 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) = (3(2sin(3π(2x^2 - 5x - 1) - 2) + 3) - 1)/(-2(2sin(3π(2x^2 - 5x - 1) - 2) + 3) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 297 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 1sin(1π(2x^2 + 3x) - 1) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 201 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 5(3sin(2π((3x - 1)/(-2x + 3)) + 3) - 2)^2 + 4(3sin(2π((3x - 1)/(-2x + 3)) + 3) - 2) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = (-2(-2sin(1π(-2|x + 1| - 1)) + 3) + 3)/(-3(-2sin(1π(-2|x + 1| - 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 minima does the function f(x) = 3sin(3π(-2x + 5) + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many local minima does the function f(x) = (-1(1sin(1πx + 3) - 2) - 3)/(-3(1sin(1πx + 3) - 2) + 2) have 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((2(2cos(3πx - 3) - 3) + 1)/(-2(2cos(3πx - 3) - 3) + 1))^2 - 5((2(2cos(3πx - 3) - 3) + 1)/(-2(2cos(3πx - 3) - 3) + 1)) + 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) = 1|((2(-5(1x + 1)^2 - 5(1x + 1) + 4) + 3)/(-2(-5(1x + 1)^2 - 5(1x + 1) + 4) + 3)) + 3| + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (2(-3(-1|(1cos(1πx + 3)) - 1| + 2) - 3) + 1)/(3(-3(-1|(1cos(1πx + 3)) - 1| + 2) - 3) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -5(-1|(-1sin(1πx + 1) - 1) + 1| - 2) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -1(3|((1(3cos(1πx - 3) - 3) - 1)/(1(3cos(1πx - 3) - 3) - 2))| - 2)^2 + 3(3|((1(3cos(1πx - 3) - 3) - 1)/(1(3cos(1πx - 3) - 3) - 2))| - 2) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 2cos(2π(-5((-1(-1|x + 2|) - 2)/(-1(-1|x + 2|) - 1))^2 - 1((-1(-1|x + 2|) - 2)/(-1(-1|x + 2|) - 1)) + 2) - 3) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 98 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -2|(4(-1((-1x - 1)/(2x - 1)) - 2)^2 + 3(-1((-1x - 1)/(2x - 1)) - 2) + 5) - 2| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 4(3|(-2sin(2πx + 2)) + 2| - 3)^2 - 3(3|(-2sin(2πx + 2)) + 2| - 3) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 2(2cos(2πx + 3) + 1)^2 + 4(2cos(2πx + 3) + 1) where -10 ≤ x ≤ 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) = 2e^(-1(3|((3x - 3)/(-1x + 2))| + 2)) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 3e^(-2(3(1((-2x + 3)/(-3x - 2))^2 + 3((-2x + 3)/(-3x - 2)) + 2) - 2)) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 52 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 1(2cos(2π(-3x^2 + 3x) - 3) + 1) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 223 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = 5(3|(4((-1x + 3)/(-2x - 2)) + 3) + 1| - 3)^2 - 5(3|(4((-1x + 3)/(-2x - 2)) + 3) + 1| - 3) - 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 4(-2sin(3πx + 3) + 1)^2 - 1(-2sin(3πx + 3) + 1) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 2(-2|(-1sin(2π((1x + 2)/(-1x + 3)) + 3) + 2) + 3|)^2 + 5(-2|(-1sin(2π((1x + 2)/(-1x + 3)) + 3) + 2) + 3|) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5(1e^(2(2|((1x - 1)/(3x + 3))| - 1)) - 3)^2 - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "How many local minima does the function f(x) = -1(4(-2|(2cos(3πx) - 3) + 1| + 2)^2 - 3(-2|(2cos(3πx) - 3) + 1| + 2)) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 59 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = -2cos(3π(-3|x + 2|) - 2) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 90 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = (-3(-1sin(1π(4x + 1) + 3) + 2))/(3(-1sin(1π(4x + 1) + 3) + 2) + 2) where -10 ≤ x ≤ 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) = -1(4(-2cos(1π((2x + 2)/(-1x + 2)) + 3) - 2) - 5)^2 - 3(4(-2cos(1π((2x + 2)/(-1x + 2)) + 3) - 2) - 5) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 44 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 1(-2sin(1π(2|x - 1| + 2)) + 2)^2 - 1(-2sin(1π(2|x - 1| + 2)) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = (-1(2sin(3πx + 1) - 1) + 2)/(-3(2sin(3πx + 1) - 1) - 2) where -10 ≤ x ≤ 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) = -3e^(-2(-1|(3x^2 + 1x + 2) + 1| + 2)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -3|(1(1sin(3π((3x + 3)/(3x + 2)) - 1)) - 2) - 2| + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -3cos(2π(-3((1(2|x + 2| - 2) - 3)/(1(2|x + 2| - 2) + 3))) + 1) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "How many local minima does the function f(x) = 2(1cos(3π(2|(3x^2 - 5) + 1| - 2) - 2) + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 256 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 2((3(1|x + 1| - 1) + 2)/(3(1|x + 1| - 1) - 2))^2 - 1((3(1|x + 1| - 1) + 2)/(3(1|x + 1| - 1) - 2)) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 2sin(2π(2((-1(3x - 3) + 1)/(-2(3x - 3) - 3))^2 + 4((-1(3x - 3) + 1)/(-2(3x - 3) - 3)) + 3) - 3) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "How many local minima does the function f(x) = 3(1cos(3π((-3x - 3)/(-3x - 2))) - 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -1|(-2cos(3πx - 2) + 1) - 3| + 2 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 maxima for the function f(x) = 2sin(1π(-2|x + 3| + 2) + 1) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 1|(-5x^2 + 3x + 2) + 3| + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "How many local minima does the function f(x) = 2cos(2π(-1x + 5)) - 2 have 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(-1|(2e^(-1x) - 2) - 1| + 1)^2 - 4(-1|(2e^(-1x) - 2) - 1| + 1) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "How many local minima does the function f(x) = -3cos(3π(2|x + 1|) + 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many local minima does the function f(x) = 1(1((-3x + 1)/(1x + 1)) + 4)^2 + 5(1((-3x + 1)/(1x + 1)) + 4) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 3sin(3π(-2x^2 - 1x - 1) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 453 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = (3(-2(2sin(3πx + 3) + 2) - 2) + 1)/(-2(-2(2sin(3πx + 3) + 2) - 2)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 3|(-1sin(2π(-5(2x - 1)^2 + 3(2x - 1) - 5)) - 3)| - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 238 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -1|(2x^2 - 5x + 1) - 3| - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5(-3|((-2(-5x - 3) + 2)/(-2(-5x - 3) + 1)) - 2| + 1)^2 - 5(-3|((-2(-5x - 3) + 2)/(-2(-5x - 3) + 1)) - 2| + 1) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 2 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -3(2|(-2((-3x)/(-3x + 4)) + 4) + 2|)^2 + 2(2|(-2((-3x)/(-3x + 4)) + 4) + 2|) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 3|(2(-1(-3sin(3πx) + 3) - 1)^2 - 2(-1(-3sin(3πx) + 3) - 1) - 5) - 2| + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-2(-4(-1|(5x^2 + 4x - 4) + 3| + 2) - 4) + 2)/(-3(-4(-1|(5x^2 + 4x - 4) + 3| + 2) - 4) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -3((-2(1|x + 1| - 2) + 1)/(1(1|x + 1| - 2)))^2 - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2|(1e^(2((-2(1x - 4))/(-2(1x - 4) + 1))) - 2) + 2| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -1e^(1(1(-1|((-2x + 1)/(-3x + 2)) + 3| + 2) - 2)) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-1(-1sin(1πx + 3)) + 1)/(-2(-1sin(1πx + 3))) have 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 minima for the function f(x) = -1|(-2cos(2πx + 3) - 3) - 1| + 1 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) = (3(-1(3sin(1πx + 2) + 1)^2 - 4(3sin(1πx + 2) + 1) + 3))/(1(-1(3sin(1πx + 2) + 1)^2 - 4(3sin(1πx + 2) + 1) + 3) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 20 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1sin(1π(2x^2 + 5x - 5) - 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 406 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2|(3(3cos(1πx - 1) + 3)^2 + 3(3cos(1πx - 1) + 3) - 5)| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 2(1|(-2sin(1πx + 2) - 3) - 3| + 2) - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = 1(5(2|((1x - 1)/(2x)) - 3| - 1) - 5)^2 - 1(5(2|((1x - 1)/(2x)) - 3| - 1) - 5) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -4(-3cos(3π(-4((-1x + 2)/(3x + 3))^2 + 3((-1x + 2)/(3x + 3)) - 3) - 1) + 3) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -2cos(2π((3(-2x + 3))/(2(-2x + 3) - 1)) + 2) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -4(-2cos(1π(5x - 4) - 3) + 3)^2 + 5(-2cos(1π(5x - 4) - 3) + 3) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -1cos(1π(-2|x + 2| - 2) + 2) - 2 where -10 ≤ x ≤ 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) = 1|(2((-1(3sin(2πx + 3) + 3) - 1)/(3(3sin(2πx + 3) + 3) - 2)) + 4) - 2| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 79 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1sin(1π(1|x - 1| + 3) + 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
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