instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Which is the biggest value? (a) 3/629 (b) -11 (c) 2/155\n | c\n | ibivibiv/math_instruct | |
Solve -4*a - 56 + 106 = 2*l + 56, 5*l - a - 7 = 0 for l.\n | 1\n | ibivibiv/math_instruct | |
Suppose -10*w**3/7 - 21134*w**2/7 + 76194*w/7 - 38106/7 = 0. Calculate w.\n | -2117, 3/5, 3\n | ibivibiv/math_instruct | |
Let s be (-10)/(-4)*(-1 - 1). Let w be ((-64)/(-33))/(-4) - 3/((-66)/(-4)). Let p = -0.8 + 4.8. What is the smallest value in w, p, s?\n | s\n | ibivibiv/math_instruct | |
Let c = -46 - -80. Let o(d) = -5*d + 18 - c + 16. Let r(t) = -t**2. What is o(r(n))?\n | 5*n**2\n | ibivibiv/math_instruct | |
Let w be 1/(-4) + -5*4/(-16). Let d be 5*6/15 - w. Sort d, -3, 2 in decreasing order.\n | 2, d, -3\n | ibivibiv/math_instruct | |
Calculate 85 - (-56 - (-42 + -131)).\n | -32\n | ibivibiv/math_instruct | |
What is ((-495)/(-30))/((-11)/(-8))?\n | 12\n | ibivibiv/math_instruct | |
Is 46797 a multiple of 19?\n | True\n | ibivibiv/math_instruct | |
Solve 32 = -s + 35 for s.\n | 3\n | ibivibiv/math_instruct | |
Let x be 1106/(-79) + 73/5. Let j be (-4)/14 + 3/(-14). Which is the second smallest value? (a) j (b) -4 (c) x\n | a\n | ibivibiv/math_instruct | |
What is 280389.87 nanoseconds in hours?\n | 0.000000077886075\n | ibivibiv/math_instruct | |
Suppose we have a system described by the Lorenz equations:
dx/dt =σ(y−x)
dy/dt =x(ρ−z)−y
dz/dt =xy−βz
where σ = 10, ρ = 28, and β = 8/3.
What is the value of x at t = 40, if it starts at x = 1 and the initial values for y and z are both 0? Round your answer to two decimal places. | To solve this problem, we need to numerically integrate the Lorenz equations using the given initial conditions and parameters. One common method for doing this is the fourth-order Runge-Kutta method. Heres a Python implementation to find the value of x at t = 40:
```python
import numpy as np
def lorenz_equations(sta... | ibivibiv/math_instruct | |
Find p, given that 4*p**5 - 16*p**4 + 8*p**3 + 16*p**2 - 12*p = 0.\n | -1, 0, 1, 3\n | ibivibiv/math_instruct | |
Let b = 29.253 - 49.4. Let z = -0.447 - b. What is z rounded to the nearest integer?\n | 20\n | ibivibiv/math_instruct | |
Round -199059.26 to the nearest one hundred.\n | -199100\n | ibivibiv/math_instruct | |
Three letters picked without replacement from hhhhhhhhhchhhhh. What is prob of picking 2 h and 1 c?\n | 1/5\n | ibivibiv/math_instruct | |
Calculate -324 divided by -6.\n | 54\n | ibivibiv/math_instruct | |
Let r(k) = 2*k + 1. Let j be -2*3/(-8)*1*-4. Calculate r(j).\n | -5\n | ibivibiv/math_instruct | |
Let k(z) be the third derivative of -11*z**7/105 - z**4/4 - 35*z**2. Find the second derivative of k(m) wrt m.\n | -264*m**2\n | ibivibiv/math_instruct | |
What is the derivative of 105*o**3 + o**2 + 171 wrt o?\n | 315*o**2 + 2*o\n | ibivibiv/math_instruct | |
Let w(h) = -4*h + 13. Let o be w(-12). Let a = -33 + o. What is the tens digit of a?\n | 2\n | ibivibiv/math_instruct | |
Let q(i) = i**3 + 4*i**2 - i - 2. Let r(w) = -2*w**2 - w + 2. Let n be r(-2). Let o be q(n). Let b(p) = 9*p**2 - 4*p + 5. List the prime factors of b(o).\n | 3, 11\n | ibivibiv/math_instruct | |
What is the closest to 1/3 in 1.161, 8, 2, 5?\n | 1.161\n | ibivibiv/math_instruct | |
Does 158/3 = 54?\n | False\n | ibivibiv/math_instruct | |
What is the third biggest value in 3/7, 5, -240/13, -1?\n | -1\n | ibivibiv/math_instruct | |
Suppose -5*z - 1 = 19. Let j = z - -25. Is j a multiple of 8?\n | False\n | ibivibiv/math_instruct | |
-29.846*0\n | 0\n | ibivibiv/math_instruct | |
Calculate 36/(-558) + ((-21408)/7440)/((-6)/5).\n | 7/3\n | ibivibiv/math_instruct | |
Expand (-4*t**4 + 5*t**4 - 2*t**4)*(33 + 8*t - 33) - 2*t**4 - t**4 + 3*t**5 - 4*t**5 + t**2.\n | -9*t**5 - 3*t**4 + t**2\n | ibivibiv/math_instruct | |
-7438 + -0.06\n | -7438.06\n | ibivibiv/math_instruct | |
Calculate -154112 divided by -32.\n | 4816\n | ibivibiv/math_instruct | |
What is the third root of 2286421 to the nearest integer?\n | 132\n | ibivibiv/math_instruct | |
Suppose 75*o - 68*o - 28 = 0. Let c(y) be the second derivative of y**5/20 + y**4/2 + y**3/2 - 3*y**2 + y. Let k be c(-5). Solve o*r - k = 2*r for r.\n | 2\n | ibivibiv/math_instruct | |
How many milliseconds are there in 3/8 of a second?\n | 375\n | ibivibiv/math_instruct | |
Divide -798 by 133.\n | -6\n | ibivibiv/math_instruct | |
List the prime factors of 625492.\n | 2, 7, 89, 251\n | ibivibiv/math_instruct | |
Let h(j) be the second derivative of 509*j**8/28 - j**4/12 + 175*j**2/2 + 123*j + 3. Find the third derivative of h(t) wrt t.\n | 122160*t**3\n | ibivibiv/math_instruct | |
b"What is the yth term of 262, 615, 970, 1327, 1686?\n" | y**2 + 350*y - 89\n | ibivibiv/math_instruct | |
What is the thousands digit of 3851913?\n | 1\n | ibivibiv/math_instruct | |
Solve 0 = 2*o + 4*b - 14, -43*o - 5*b = -39*o - 16 for o.\n | -1\n | ibivibiv/math_instruct | |
In base 12, what is -779a6 - -1?\n | -779a5\n | ibivibiv/math_instruct | |
(-86)/((-3096)/5292) - 230\n | -83\n | ibivibiv/math_instruct | |
Let u(q) = 191*q - 192. Let o be u(1). Which is the fourth biggest value? (a) 2/5 (b) 0.53 (c) o (d) -0.1\n | c\n | ibivibiv/math_instruct | |
What is the highest common divisor of 54 and 27558?\n | 18\n | ibivibiv/math_instruct | |
Simplify -5 + (sqrt(171) + -2 + -4 + (sqrt(19) - (sqrt(19) - sqrt(19)*-3*4))*-5)**2.\n | -756*sqrt(19) + 75442\n | ibivibiv/math_instruct | |
Simplify 3*(sqrt(72) + ((sqrt(72) + -2)*-1 - sqrt(72)))*-6.\n | -36 + 108*sqrt(2)\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(-53.2483 % 37.1448) - (-32.7886 + 91.3866) | -37.5567 | ibivibiv/math_instruct | |
Suppose 3*v - 5*u + 127 - 132 = 0, 5*v - 2*u - 21 = 0. Let w(z) = -8*z. Let g be w(1). Let x = 13 + g. Solve 7 = -5*r + t, 3*r - v - 2 = -x*t for r.\n | -1\n | ibivibiv/math_instruct | |
Simplify (5*-6*sqrt(117)*2 + (5 + sqrt(117) + -1)*-3)**2.\n | 4536*sqrt(13) + 464517\n | ibivibiv/math_instruct | |
Which is the closest to -3? (a) 3 (b) 99 (c) 0.03 (d) -2/21\n | d\n | ibivibiv/math_instruct | |
Let d(n) = 55*n**2 - 8*n + 21. Let i(s) = -32*s**2 + 4*s - 9. Determine -3*d(q) - 5*i(q).\n | -5*q**2 + 4*q - 18\n | ibivibiv/math_instruct | |
What is next in 189853, 189866, 189881, 189898?\n | 189917\n | ibivibiv/math_instruct | |
Suppose -4*m + 4 + 4 = 0. Suppose 4*f - 5*l + 17 = 3*f, 3*l - 6 = m*f. Suppose -18 = f*v - v. Round v to the nearest ten.\n | -10\n | ibivibiv/math_instruct | |
Expand (-2*k**2 - 2*k**2 + 2*k**2)*(k - 4*k + 4*k) + (-k + 0*k - k)*(41*k - 41*k + 40*k**2).\n | -82*k**3\n | ibivibiv/math_instruct | |
Round 549487260 to the nearest one million.\n | 549000000\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 d and 1 a when two letters picked without replacement from {a: 3, d: 9}.\n | 9/22\n | ibivibiv/math_instruct | |
What is (-2)/(-20)*-2*-40?\n | 8\n | ibivibiv/math_instruct | |
30 (base 11) to base 10\n | 33\n | ibivibiv/math_instruct | |
What is prob of picking 2 h when two letters picked without replacement from aaahha?\n | 1/15\n | ibivibiv/math_instruct | |
Evaluate (158/79)/(-2*2/(-6)).\n | 3\n | ibivibiv/math_instruct | |
What is the next term in 192, 155, 122, 93, 68?\n | 47\n | ibivibiv/math_instruct | |
Suppose y - 48 = 4*y. Let o be (y/3)/(2/(-12)). Let b be (-2)/(-5) + o/20. Solve -6*s + 4*s = -b for s.\n | 1\n | ibivibiv/math_instruct | |
Calculate the smallest common multiple of 1176 and 441.\n | 3528\n | ibivibiv/math_instruct | |
Let n be (-41)/(-43) - (37468/(-1247) - -30). Put n, 3, -2105 in decreasing order.\n | 3, n, -2105\n | ibivibiv/math_instruct | |
What is 153 minutes after 5:19 PM?\n | 7:52 PM\n | ibivibiv/math_instruct | |
Let l(z) = -z**3 + 6*z**2 - 22*z + 77. Let p be l(4). Suppose 19 = o + 5. Let q be (1 - 4)*o/(-6). Calculate the highest common factor of q and p.\n | 7\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {g: 4, o: 1, r: 6, s: 1, b: 3, h: 4}. What is prob of picking 1 g and 1 h?\n | 16/171\n | ibivibiv/math_instruct | |
(1/(-44))/(240/960)\n | -1/11\n | ibivibiv/math_instruct | |
Solve 175*s = 159*s for s.\n | 0\n | ibivibiv/math_instruct | |
What is next in 662, 823, 1092, 1469, 1954?\n | 2547\n | ibivibiv/math_instruct | |
Expand (0*h - h + 7*h + h - 5 + 5 + (-3 - 3 + 5)*(-2*h + 4*h - 3*h) + 18*h + 78 - 78)*(-h**2 - h**2 + h**2).\n | -26*h**3\n | ibivibiv/math_instruct | |
Calculate the remainder when 644 is divided by 24.\n | 20\n | ibivibiv/math_instruct | |
Let i(v) be the first derivative of -2*v**2 - 35*v - 3913. Calculate i(-12).\n | 13\n | ibivibiv/math_instruct | |
Which is smaller: 2/153 or 0?\n | 0\n | ibivibiv/math_instruct | |
Let v = 11 + -6. Suppose -3*q + 4*q - 4*c = v, 2*c = 4. What is the remainder when 51 is divided by q?\n | 12\n | ibivibiv/math_instruct | |
What is the third derivative of -c**5 + 4*c**4 - 41*c**3 + 13520*c**2 wrt c?\n | -60*c**2 + 96*c - 246\n | ibivibiv/math_instruct | |
Is 18398 a prime number?\n | False\n | ibivibiv/math_instruct | |
Let a(f) = -11*f**2 + 8*f - 11. Let r be ((-4)/(-1))/((-10)/(-20)). Let j = -3 + 9. Let z(w) = -j + 2 + 3*w - 4*w**2 - 1 + 1. Calculate r*z(s) - 3*a(s).\n | s**2 + 1\n | ibivibiv/math_instruct | |
Calculate the greatest common divisor of 35682 and 171.\n | 57\n | ibivibiv/math_instruct | |
Let s(f) be the third derivative of -f**5/240 - f**4/24 - f**3/8 + 25*f**2. Factor s(c).\n | -(c + 1)*(c + 3)/4\n | ibivibiv/math_instruct | |
Convert 20773541 (base 9) to base 6.\n | 554533101\n | ibivibiv/math_instruct | |
What is the nearest to 2/119 in -11, 0.4, 1, 0.3, -10?\n | 0.3\n | ibivibiv/math_instruct | |
(4/(-24)*-14)/(27/81)\n | 7\n | ibivibiv/math_instruct | |
Let t(x) = -x**3 + 11*x**2 - 18*x - 44. What is t(8)?\n | 4\n | ibivibiv/math_instruct | |
Does 10 divide 43705683?\n | False\n | ibivibiv/math_instruct | |
Calculate the smallest common multiple of 152 and 190.\n | 760\n | ibivibiv/math_instruct | |
Simplify -5*(-4 + sqrt(20) + sqrt(20) + (sqrt(500) + 0)**2).\n | -2480 - 20*sqrt(5)\n | ibivibiv/math_instruct | |
Sort 1, 14, 50, 4, 2 in increasing order.\n | 1, 2, 4, 14, 50\n | ibivibiv/math_instruct | |
Let c(i) = -i**3 + 11*i**2 - 12*i + 13. Let w(j) = -j**2 + j - 2. Let z(g) = -c(g) - 5*w(g). Let l be z(5). Are l and 2 unequal?\n | True\n | ibivibiv/math_instruct | |
Solve 33*l - 4*l + 0*l = 58 for l.\n | 2\n | ibivibiv/math_instruct | |
Simplify 4 + (sqrt(1300) + -4 - sqrt(1300)) + (4*(sqrt(1300) + -4 + sqrt(1300)))**2.\n | -2560*sqrt(13) + 83456\n | ibivibiv/math_instruct | |
Suppose 2*c - 11274 = -3*w, -c + 555 = 5*w - 5089. What are the prime factors of c?\n | 2, 3, 313\n | ibivibiv/math_instruct | |
Suppose 85 = 4*m + 21. Let b = -15 + m. Does 15 divide ((-9)/(-12))/(b/40)?\n | True\n | ibivibiv/math_instruct | |
Let g(h) = -4*h**2 + 4*h + 2. Let p(z) be the third derivative of 1/12*z**4 + 1/6*z**3 - 58*z**2 + 0*z - 1/30*z**5 + 0. Determine 3*g(y) - 7*p(y).\n | 2*y**2 - 2*y - 1\n | ibivibiv/math_instruct | |
Collect the terms in -804*v**2 - 596*v**2 + 2 - 2.\n | -1400*v**2\n | ibivibiv/math_instruct | |
b"What is the kth term of 3047, 2187, 761, -1231, -3789, -6913, -10603?\n" | -283*k**2 - 11*k + 3341\n | ibivibiv/math_instruct | |
Calculate prob of sequence xx when two letters picked without replacement from {o: 7, x: 7}.\n | 3/13\n | ibivibiv/math_instruct | |
What is the ten thousands digit of 1519343578?\n | 4\n | ibivibiv/math_instruct | |
Collect the terms in -2886*j**2 - 4 - 6*j - 19 + 24 + 8*j + 13088*j**2.\n | 10202*j**2 + 2*j + 1\n | ibivibiv/math_instruct |
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