messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3|((-3(-2sin(1πx - 2) + 2) + 2)/(2(-2sin(1πx - 2) + 2) + 1)) - 1| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2sin(2π(2|(3x^2 - 2x + 5) - 1|) + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 484 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -3|(-4(-3x^2 - 2x)^2 - 4(-3x^2 - 2x) + 1) + 1| + 3 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) = 1sin(3π(-4(1x - 1) - 2) - 1) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -2sin(3π(-4(-4x + 2)^2 + 3(-4x + 2) - 3)) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 390 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -2sin(1π(3(-5x + 4)^2 - 2(-5x + 4) + 4) - 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 221 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -1sin(3π(-1(-4x^2 + 3x - 2) + 5) - 2) + 2 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) = -2(2e^(-1(-5x + 1)) - 2) - 2 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) = 1cos(1π(-2|(-1|x - 3| - 3) + 3| + 2) - 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 1sin(1π(1(5x - 2) - 4) + 1) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = -1|(-1|(-1cos(1πx + 2) + 2) + 2| - 1) - 2| + 2 where -10 ≤ x ≤ 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|(2cos(2π(2x + 3) + 1) + 3) - 1| - 3 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) = -3(1sin(3π(3x^2 - 5x) - 2)) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 259 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1cos(3π(3(2|x + 3| - 1) + 1) - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 361 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = -3cos(3π(1(-2x^2 - 2x + 2)^2 - 2(-2x^2 - 2x + 2) - 2) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 118 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -1|((-3(2cos(3πx - 1) - 3) - 1)/(-2(2cos(3πx - 1) - 3) + 1)) + 3| - 3 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) = 2|(-1cos(3π(5x^2 + 4) + 3) - 3) + 1| + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 248 | MATH |
[
{
"content": "How many local minima does the function f(x) = 1(2cos(3π(2x + 1) - 2) + 2) + 2 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 maxima for the function f(x) = 2(1sin(3π(2x + 5) + 1) - 1) + 4 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) = -3(-1cos(2π((2x - 1)/(-2x - 1)) + 1) - 3)^2 - 3(-1cos(2π((2x - 1)/(-2x - 1)) + 1) - 3) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 3|(5(-3cos(2πx - 1) + 2)^2 + 1(-3cos(2πx - 1) + 2) - 3)| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 159 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -1(-2cos(2π(-4x^2 + 5x + 1) - 2) - 3)^2 + 1(-2cos(2π(-4x^2 + 5x + 1) - 2) - 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 517 | MATH |
[
{
"content": "How many local minima does the function f(x) = 3|((1(3cos(2πx - 2) + 1) + 2)/(2(3cos(2πx - 2) + 1) - 3)) - 3| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "How many local minima does the function f(x) = 2(2cos(2π((3x)/(1x + 1)) - 1) - 3)^2 - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = (-3((3(2sin(1πx + 2) + 3))/(-3(2sin(1πx + 2) + 3) + 4)) + 1)/(-1((3(2sin(1πx + 2) + 3))/(-3(2sin(1πx + 2) + 3) + 4))) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 3sin(3π(1((-3x - 2)/(-3x + 1))^2 + 4((-3x - 2)/(-3x + 1)) + 4) - 2) + 3 where -10 ≤ x ≤ 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) = -3|(-2cos(3π(-3x - 2) - 3) - 2)| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 90 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -3cos(1π(-3((2x - 2)/(-1x + 3)) - 4) + 3) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = (1(-2(-3cos(1πx + 2) + 1)^2 - 3(-3cos(1πx + 2) + 1) - 1) - 3)/(1(-2(-3cos(1πx + 2) + 1)^2 - 3(-3cos(1πx + 2) + 1) - 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 40 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 4(-5(-1sin(3πx - 1) + 3)^2 - 1(-1sin(3πx - 1) + 3) - 1) + 4 where -10 ≤ x ≤ 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) = (-1(1|(-1cos(2πx + 1) + 3)|) + 3)/(-2(1|(-1cos(2πx + 1) + 3)|) + 3) 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 maximum points for f(x) = -1cos(2π((3(-3|x + 3| - 1) - 3)/(-1(-3|x + 3| - 1) - 1)) - 2) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = -1sin(1π(4(4x + 1)^2 + 5(4x + 1) - 2)) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 233 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 1|(2(1|x + 2|)^2 - 4(1|x + 2|) - 2) - 1| - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -1|(-3cos(2π(4x^2 - 3) - 1) + 2) + 2| - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 268 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -3(1(2cos(3πx + 2) + 1) + 4)^2 + 1(1(2cos(3πx + 2) + 1) + 4) + 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 3(-2sin(1π(-3x + 4) + 3) + 3) - 2 have 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 maxima for the function f(x) = -3(1|(-4x^2 - 4x) + 2| - 3)^2 - 1(1|(-4x^2 - 4x) + 2| - 3) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 1(2cos(1π((1x + 3)/(2x)) - 1))^2 - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 1sin(3π(-3((-2x + 2)/(2x - 1))^2 + 3((-2x + 2)/(2x - 1)) - 5) + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 3(-5(-3sin(1πx + 2) + 2) - 4) - 2 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(-2cos(1π(-3|x + 2| - 1) + 3) - 1) - 1)/(-3(-2cos(1π(-3|x + 2| - 1) + 3) - 1) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 117 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1|(-1|(3cos(2πx + 1) - 3) - 1| - 3)| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (-3(1cos(1π(-1|x - 1|) - 3)) + 3)/(3(1cos(1π(-1|x - 1|) - 3)) - 1) 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 minimum points for f(x) = -2sin(2π(3(2x + 3) + 4) - 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -1((-3(1sin(1πx + 3)) - 2)/(3(1sin(1πx + 3))))^2 + 1((-3(1sin(1πx + 3)) - 2)/(3(1sin(1πx + 3)))) - 5 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) = -3cos(2π(3(3x + 4) + 1) - 2) - 1 have 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) = 5(1|(-3cos(1πx + 3)) - 1| - 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 5(1cos(2π(1|x + 1| - 2) - 2) + 2) - 4 where -10 ≤ x ≤ 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) = -1|(2e^(1(1x^2 + 2x - 5)) - 1) - 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) = -1(-3(-4x^2 + 1x + 4)^2 + 3(-4x^2 + 1x + 4) - 1)^2 - 4(-3(-4x^2 + 1x + 4)^2 + 3(-4x^2 + 1x + 4) - 1) 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) = -5(-2cos(1π(-3|x + 2| + 3) + 3))^2 + 3 where -10 ≤ x ≤ 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(-1sin(1π(2|x - 2| + 1) + 3) + 3) + 2)/(1(-1sin(1π(2|x - 2| + 1) + 3) + 3) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 1|(-1sin(3π(-1x^2 - 3x - 3) - 2) - 1) + 1| + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 479 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -3cos(1π(-2(-4x^2 - 1x + 2) - 3) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 263 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -1(2(-2sin(1πx) + 1) + 2)^2 + 2(2(-2sin(1πx) + 1) + 2) - 5 where -10 ≤ x ≤ 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) = (-2(3sin(2π(-1x) - 1) - 3) + 1)/(1(3sin(2π(-1x) - 1) - 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) = -2sin(3π(3(-1|x - 3| - 1)^2 - 3) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 262 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -2sin(2π(-1|(2x + 3) - 1| + 1) + 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 81 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 2(2|(3cos(3πx + 3) + 2) + 3| + 1)^2 - 1(2|(3cos(3πx + 3) + 2) + 3| + 1) + 5 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 maxima for the function f(x) = (-1(1cos(3π(2x) + 3) + 2) - 1)/(-3(1cos(3π(2x) + 3) + 2) + 1) 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) = -5(1sin(1π(-2x^2 - 5x + 5) + 2) - 2)^2 - 4(1sin(1π(-2x^2 - 5x + 5) + 2) - 2) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 192 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 4(3|(3sin(2πx + 1) + 2) + 2| - 2) + 5 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) = (1(1sin(3π(3x + 2) - 1) - 3) - 3)/(-3(1sin(3π(3x + 2) - 1) - 3) + 4) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 90 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 2cos(1π(5(-2|x - 1|) - 1)) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 200 | MATH |
[
{
"content": "How many local minima does the function f(x) = -5(1sin(1π(1x^2 + 2x - 2) + 3) + 3)^2 - 3(1sin(1π(1x^2 + 2x - 2) + 3) + 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 102 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 2|(-4(2sin(3πx + 1) - 3)^2 - 2(2sin(3πx + 1) - 3) + 4) - 2| + 1 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) = 4(1sin(2π(-5x - 2) - 1) - 3) + 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = -1|(-1(3cos(2πx - 3) + 2) + 2) + 1| + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "How many local minima does the function f(x) = (-1(-1cos(1π(1x) - 3) - 3))/(-1(-1cos(1π(1x) - 3) - 3) + 3) 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) = -3sin(3π(-4(2|x + 3| - 3)^2 + 3) + 1) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 238 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3(-2|(3cos(1πx + 2) + 1) - 1| + 1)^2 + 5(-2|(3cos(1πx + 2) + 1) - 1| + 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (-2(-3e^(1(2|x - 3| + 1)) + 2))/(3(-3e^(1(2|x - 3| + 1)) + 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 5(-4(-1|x + 3| + 3)^2 - 5(-1|x + 3| + 3))^2 - 4(-4(-1|x + 3| + 3)^2 - 5(-1|x + 3| + 3)) + 5 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 minimum points for f(x) = 1(1cos(3π((-2x - 1)/(2x + 3))) + 1)^2 + 4(1cos(3π((-2x - 1)/(2x + 3))) + 1) - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = (-2(-1cos(3π(3x + 1))))/(2(-1cos(3π(3x + 1))) + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 108 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = (3((3(2x - 4) + 3)/(-2(2x - 4) - 2)) + 2)/(1((3(2x - 4) + 3)/(-2(2x - 4) - 2)) + 2) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -3(3(-1cos(3πx - 1) + 3)^2 + 5(-1cos(3πx - 1) + 3) - 4)^2 + 1(3(-1cos(3πx - 1) + 3)^2 + 5(-1cos(3πx - 1) + 3) - 4) - 5 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) = 3|(5(-4x^2 + 2x + 5)^2 - 4) - 1| where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -3sin(2π(2(-5x^2 - 4x - 3) + 2) - 2) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 493 | MATH |
[
{
"content": "How many local minima does the function f(x) = -4(1(2sin(3πx + 3) - 2)^2 + 5(2sin(3πx + 3) - 2) - 4)^2 - 5(1(2sin(3πx + 3) - 2)^2 + 5(2sin(3πx + 3) - 2) - 4) - 2 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) = -1|(-1sin(2π(-4x - 4) - 1) - 2) - 2| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = (-3(-2(2e^(-2x) + 3)^2 + 2(2e^(-2x) + 3) + 1) - 2)/(-2(-2(2e^(-2x) + 3)^2 + 2(2e^(-2x) + 3) + 1) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 74 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = (2(3sin(2π(-5x - 5) + 1) - 1) + 2)/(1(3sin(2π(-5x - 5) + 1) - 1) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 101 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 2(-4(2cos(1πx - 3) - 2)^2 + 1(2cos(1πx - 3) - 2) - 4) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 3cos(2π(-5(2|x + 3| + 3)) - 1) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 401 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -3(-3(-3cos(2πx + 3) + 1)) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 1(-2sin(1π(-5x - 5)) - 1)^2 - 3(-2sin(1π(-5x - 5)) - 1) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -1sin(1π((1(1x - 4) + 3)/(3(1x - 4) - 1)) + 1) 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) = 3|(-1|(2cos(3πx - 2)) - 1|) - 3| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 119 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -3sin(2π((-1(-3|x + 2| + 1) + 2)/(3(-3|x + 2| + 1) + 2)) - 3) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 2|(3cos(2π(-2x^2 - 1x - 1) + 3)) - 3| + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 286 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -3(-2sin(3π(-4x^2 - 2x) - 1) - 1)^2 - 5(-2sin(3π(-4x^2 - 2x) - 1) - 1) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 252 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 3|(-3sin(1π(-3x^2 - 4x - 5) - 2) - 2)| - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 498 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2cos(2π((2(-2|x + 2| + 1))/(-3(-2|x + 2| + 1))) - 2) - 1 have in the interval [-10, 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) = -3(-1|(2cos(2πx + 1) + 1)| - 1)^2 - 5(-1|(2cos(2πx + 1) + 1)| - 1) have 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) = -3cos(1π(-2(3x^2 + 4) - 3) + 2) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 225 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (3(4(-1sin(1πx - 2) - 2)) + 2)/(2(4(-1sin(1πx - 2) - 2)) - 1) 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) = (-2(-3sin(2π(-4x^2 + 3x) + 2) + 2) - 1)/(-1(-3sin(2π(-4x^2 + 3x) + 2) + 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 523 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3|(2|(-2cos(1πx + 2) - 3) - 1|) - 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
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