messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the number of local minimum points for f(x) = -2sin(3π(3|(1|x - 2| + 3) - 2| + 3) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 91 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 5(-2cos(1π(2|x - 3| + 1) - 3) + 1) + 4 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) = -1|(1|(-1cos(2πx + 3) - 2) + 2| + 3) - 2| + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 69 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 2cos(3π(-1|((-1x - 1)/(-2x + 1)) + 1| + 1)) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 4(2|(2cos(1πx + 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 extrema (minima and maxima combined) does the function f(x) = 2|(1sin(3π(2x) + 3) + 1) - 2| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "How many local minima does the function f(x) = -1((-1(2sin(2πx) - 1) + 1)/(3(2sin(2πx) - 1) + 3))^2 + 3((-1(2sin(2πx) - 1) + 1)/(3(2sin(2πx) - 1) + 3)) 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) = 3cos(2π(1|(2|x - 2| - 3) - 1| - 3) - 2) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 83 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2(-1(1|x - 2| - 3)^2 + 5(1|x - 2| - 3) + 4)^2 + 4 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(-1(3sin(2πx + 2) + 3)^2 + 5(3sin(2πx + 2) + 3) + 4) - 1)/(2(-1(3sin(2πx + 2) + 3)^2 + 5(3sin(2πx + 2) + 3) + 4) - 3) 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) = (3(-4(1cos(3πx + 1)) + 1) - 1)/(1(-4(1cos(3πx + 1)) + 1) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 1|(-1(3sin(1πx + 1))^2 + 4(3sin(1πx + 1)) - 5) + 3| - 3 have in the interval [-10, 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) = (2(-3cos(1π(-5x + 1) - 2) + 2) + 2)/(2(-3cos(1π(-5x + 1) - 2) + 2) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 52 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1|(-1sin(1π(5x - 2) - 1) + 3)| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100 | MATH |
[
{
"content": "How many local minima does the function f(x) = -1(1|(2sin(1πx + 3)) + 2| - 2) + 4 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) = 4(2|(1cos(1πx - 1) + 2) + 3|)^2 + 5(2|(1cos(1πx - 1) + 2) + 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) = -4(3(-1sin(3πx - 2) - 2) - 5) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 3(-1sin(2π(2x - 1) + 3) - 3) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -3|((-1(2sin(3πx + 3) + 2) - 3)/(-1(2sin(3πx + 3) + 2) + 3)) - 2| + 3 have 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) = 5(1(3cos(1πx) - 3)^2 - 5(3cos(1πx) - 3) + 5)^2 - 3(1(3cos(1πx) - 3)^2 - 5(3cos(1πx) - 3) + 5) + 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) = -3(-3cos(1π(-3x^2 + 1x + 1) - 3))^2 + 2(-3cos(1π(-3x^2 + 1x + 1) - 3)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 222 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1|(1(-3cos(3πx - 2) - 3)) + 1| 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(-2cos(1π(-3|x - 2| + 1) - 1) + 3) - 2)/(3(-2cos(1π(-3|x - 2| + 1) - 1) + 3) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -2cos(3π(-4(1x + 1)^2 - 5(1x + 1) - 2) + 1) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 251 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 1(3sin(1π((-2x + 3)/(1x + 2)) - 1) + 1) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 51 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1|(2sin(1π(-2x + 3) - 3) + 3) - 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 2(2(-1cos(3πx - 3) - 3)^2 - 2) - 5 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) = -1sin(3π(4(-3|x - 3| - 1) + 3) - 2) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 360 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (3(1sin(1π(-4x^2 - 3x - 1) + 1) + 2) - 1)/(-2(1sin(1π(-4x^2 - 3x - 1) + 1) + 2) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 328 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = (-2(-5(-3sin(3πx + 2) - 3) + 2) + 1)/(3(-5(-3sin(3πx + 2) - 3) + 2) + 2) where -10 ≤ x ≤ 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(3π((-1x + 3)/(-3x + 4)) + 3) - 2) - 3| + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = (-2(-1e^(-2((-3x - 3)/(-3x))) + 3) - 3)/(3(-1e^(-2((-3x - 3)/(-3x))) + 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 minimum points for f(x) = -1|((3(-1x^2 + 4x + 3) - 2)/(-2(-1x^2 + 4x + 3))) - 1| - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "How many local minima does the function f(x) = -5((-1(3sin(3πx) - 2) + 3)/(-3(3sin(3πx) - 2) - 1)) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -2|((-1(-2sin(3πx + 1) + 3) - 3)/(-3(-2sin(3πx + 1) + 3) - 2)) + 1| - 2 where -10 ≤ x ≤ 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) = 3|(3cos(2π((-2x - 2)/(-3x - 2)) - 3) - 3) - 2| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3cos(3π(5((-1x - 1)/(3x - 1))^2 - 3((-1x - 1)/(3x - 1)) + 3)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 53 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -1sin(1π(1(3x + 1) + 4) + 3) + 1 have in the interval [-10, 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) = 1(3cos(3π(-2|x - 1|) + 3) + 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 61 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 2sin(3π(1(2x - 2)^2 - 2(2x - 2) - 1) - 2) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 253 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 1sin(2π(-1(2x + 3)^2 + 4(2x + 3) - 5)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 267 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -2cos(3π(5(-1|x + 1| + 2) - 1) + 1) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 152 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 1cos(2π((-2((2x + 2)/(-2x)) + 1)/(1((2x + 2)/(-2x)) + 3)) + 2) + 3 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) = 1cos(1π(-2|((3x + 2)/(-1x)) + 1| - 2) - 1) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 47 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 1e^(1(5(-3x^2 + 4)^2 + 4(-3x^2 + 4) + 4)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many local minima does the function f(x) = 5((1(-3sin(1πx - 2) - 3) - 2)/(-2(-3sin(1πx - 2) - 3) - 1))^2 + 3((1(-3sin(1πx - 2) - 3) - 2)/(-2(-3sin(1πx - 2) - 3) - 1)) - 4 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 maxima for the function f(x) = 1cos(2π(2|(3|x + 2| - 1) + 2| + 1) + 1) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 2cos(3π(2|(4x + 1) - 2| - 2) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -2|(2|(2sin(1πx + 2) + 2) + 2|) + 1| - 3 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(2sin(1π((1x + 2)/(-1x - 3)) + 2) - 1)^2 + 2(2sin(1π((1x + 2)/(-1x - 3)) + 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -2cos(1π(-4(-1|x + 2| - 2) - 5) - 1) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 81 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -1sin(2π(1|((2x - 2)/(-3x)) + 3| + 3) + 1) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -2|(-2(-1sin(1πx - 2))^2 + 5(-1sin(1πx - 2)) - 5) - 2| + 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) = -3(-3cos(1π(-3|x - 3|) - 3) + 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 61 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 1(2(2cos(1πx - 1) + 3) - 4) + 1 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) = 1(2cos(2π(3x^2 - 3x - 1)) - 1)^2 + 3(2cos(2π(3x^2 - 3x - 1)) - 1) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 227 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = (-1((2(3sin(3πx - 1) + 1))/(2(3sin(3πx - 1) + 1) + 2)) + 2)/(-3((2(3sin(3πx - 1) + 1))/(2(3sin(3πx - 1) + 1) + 2)) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -1sin(2π(-2|(5x + 1) - 1| - 2) - 1) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 201 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -3(5(1x^2 - 4x - 4)^2 + 4(1x^2 - 4x - 4))^2 - 1(5(1x^2 - 4x - 4)^2 + 4(1x^2 - 4x - 4)) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 1(-4(-2cos(2πx + 3) - 1)^2 - 5(-2cos(2πx + 3) - 1) + 2) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = (1(1(2cos(3πx - 3) + 2) - 1) - 2)/(2(1(2cos(3πx - 3) + 2) - 1) - 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) = (-3(1sin(2π(-1|x - 3| + 2) - 2)))/(2(1sin(2π(-1|x - 3| + 2) - 2)) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 1(2sin(1π(-4x + 1) - 2) - 1)^2 - 1(2sin(1π(-4x + 1) - 2) - 1) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = (2(3sin(2π((1x + 3)/(1x - 2)) + 3) - 2) - 2)/(1(3sin(2π((1x + 3)/(1x - 2)) + 3) - 2)) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 65 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -2e^(-1(-3(2x - 1) - 2)) + 2 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 maxima for the function f(x) = 2sin(2π((2(1x^2 + 2x - 1) + 1)/(-2(1x^2 + 2x - 1) + 3)) + 3) + 2 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) = -4(-1|(-1cos(3πx + 2)) + 3| - 3)^2 - 4(-1|(-1cos(3πx + 2)) + 3| - 3) - 4 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|((3(-1sin(3πx + 2) - 3) + 1)/(-2(-1sin(3πx + 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": "How many local extrema (minima and maxima combined) does the function f(x) = 2(2sin(1π(-3x + 4) - 3) + 1)^2 - 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) = 3|((-2(1x^2 + 5x - 5) - 1)/(-3(1x^2 + 5x - 5) + 1)) + 1| + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = (-3((-3(-2cos(1πx - 1) - 3))/(-2(-2cos(1πx - 1) - 3))) + 3)/(-3((-3(-2cos(1πx - 1) - 3))/(-2(-2cos(1πx - 1) - 3))) - 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 96 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 3(5(-2sin(2πx + 3) + 2) + 3) + 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 2cos(2π(-3(5x - 3)^2 + 1(5x - 3) + 4) - 3) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 208 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3|(-1cos(1π(-1|x| + 3) + 2) - 3) - 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = (1(-5(1sin(2πx + 3) + 3)^2 + 1(1sin(2πx + 3) + 3) + 5) + 2)/(-2(-5(1sin(2πx + 3) + 3)^2 + 1(1sin(2πx + 3) + 3) + 5)) 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) = 3cos(3π(-1(-5x^2 + 1x + 3) + 5) + 2) + 1 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) = -1cos(2π(3(5x - 2)^2 - 4(5x - 2) - 1) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 426 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 2(1|(-3cos(1πx + 2) - 2) + 3|)^2 + 3(1|(-3cos(1πx + 2) - 2) + 3|) + 2 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) = -1|(-3|(-2cos(1πx - 3) + 3) + 2| - 2) - 1| - 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 minima does the function f(x) = 2cos(1π(-1((2x + 1)/(-2x - 2))^2 - 4((2x + 1)/(-2x - 2)) - 1) + 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -2sin(3π(-2(1x^2 - 5x - 1) - 3) - 2) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 519 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -3cos(1π(1(1x)^2 - 2(1x)) - 3) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 203 | MATH |
[
{
"content": "How many local minima does the function f(x) = 1(3sin(1π(5x + 3) - 1) - 1)^2 - 2(3sin(1π(5x + 3) - 1) - 1) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1|(4(-2|x - 2| + 2)^2 - 4(-2|x - 2| + 2) - 5) - 2| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = (-2(2(3cos(3πx - 1) - 1)^2 + 5(3cos(3πx - 1) - 1) - 4))/(-2(2(3cos(3πx - 1) - 1)^2 + 5(3cos(3πx - 1) - 1) - 4) - 2) where -10 ≤ x ≤ 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) = 3cos(3π(5(-2x^2 + 1x + 2) + 3) - 3) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 237 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -5(-2sin(3π((2x - 3)/(2x + 1)) + 3) + 3) + 4 where -10 ≤ x ≤ 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) = 3sin(3π(-2|(3|x - 2| - 3) + 2|)) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 363 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1(2sin(1π(-1|x + 2|) - 3) + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -5(-2cos(1π(3x + 1) + 3) - 2)^2 - 3(-2cos(1π(3x + 1) + 3) - 2) - 4 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(-3cos(3π(2|x| - 1) - 3) + 2) - 3)/(-1(-3cos(3π(2|x| - 1) - 3) + 2) - 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 121 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 3sin(1π(1(-3|x - 1| + 3) - 3)) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2cos(1π(1(-4x + 3) - 3)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -3sin(1π(1|(3|x + 1| - 2) + 2| + 2) - 1) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = (3(-1e^(-2(-5x^2 - 4)) - 1) - 1)/(-1(-1e^(-2(-5x^2 - 4)) - 1) - 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 3|(-2(-3sin(3πx - 3) + 2) - 2) - 2| + 2 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) = 3|(-2sin(1π(-3x^2 + 4x + 5) - 2) + 3) + 1| + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 564 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -4(-1cos(3π(-1x^2 - 3x - 4) - 1) - 1) - 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 555 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3cos(2π(-5(-1x^2 + 4x + 1))) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 500 | MATH |
[
{
"content": "How many local minima does the function f(x) = (2(2sin(3π(-1|x - 2| + 3) + 3) + 2) - 1)/(-3(2sin(3π(-1|x - 2| + 3) + 3) + 2) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
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