instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Evaluate 16 + -21 - (9 - (0 + 4)).\n | -10\n | ibivibiv/math_instruct | |
What is the next term in 299, 2447, 8323, 19805, 38771, 67099, 106667?\n | 159353\n | ibivibiv/math_instruct | |
Is 4*(36 + -3)*(-888)/(-18) a multiple of 176?\n | True\n | ibivibiv/math_instruct | |
Simplify 5 + ((sqrt(165)/(sqrt(6)/sqrt(2)) - (-1*sqrt(550))/sqrt(10))/(sqrt(5)*2*1 + sqrt(5) + sqrt(40)/(sqrt(288) - sqrt(8))))**2.\n | 595/64\n | ibivibiv/math_instruct | |
Total of -532 and -10.4.\n | -542.4\n | ibivibiv/math_instruct | |
Let g = 20.7 + -17.7. What is the closest to g in 4, 1/3, 0.2?\n | 4\n | ibivibiv/math_instruct | |
What are the prime factors of 9342171?\n | 3, 1038019\n | ibivibiv/math_instruct | |
Let n be (0 + 2)*34/4. Let d = -38781 + 39172. Calculate the highest common factor of n and d.\n | 17\n | ibivibiv/math_instruct | |
Does 7 divide 371?\n | True\n | ibivibiv/math_instruct | |
b"What is the xth term of 4832, 9643, 14440, 19217, 23968?\n" | -x**3 - x**2 + 4821*x + 13\n | ibivibiv/math_instruct | |
Is 10104942 smaller than -2?\n | False\n | ibivibiv/math_instruct | |
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"# Formatting an equation: X^Y to pow(X,Y)
I am trying to solve for the intersection of two circles with arbitrary centers and arbitrary radii.
(x-X1)^2+(y-Y1)^2==R1^2
(x-X2)^2+(y-Y2)^2==R2^2
Solve[% && %%,{x,y}]
It takes ... | The task at hand involves solving for the intersection points of two circles with arbitrary centers and radii using Mathematica, and then converting any instances of exponentiation (e.g., X^Y) to the equivalent function notation (pow(X,Y)) for compatibility with OpenSCAD. Here, we delve deeper into the steps required ... | ibivibiv/math_instruct | |
Let p = -884.389 - -886. What is p rounded to 1 decimal place?\n | 1.6\n | ibivibiv/math_instruct | |
What is the smallest common multiple of 556628 and 1184?\n | 4453024\n | ibivibiv/math_instruct | |
Suppose 2*a + 4 = 8. Calculate the common denominator of 2 + 0 - a/(-4) and ((-99)/(-374))/(6/7 - 0).\n | 68\n | ibivibiv/math_instruct | |
Let q = -14 + 12. Let y = 14 - q. Is 12 a factor of y?\n | False\n | ibivibiv/math_instruct | |
What comes next: 36, 74, 116, 162, 212, 266?\n | 324\n | ibivibiv/math_instruct | |
Let q(g) = -g**2 + 5*g. Let t be q(5). Let x(s) = -4*s + 5. Let p be x(t). Solve -4*c + p = c for c.\n | 1\n | ibivibiv/math_instruct | |
Simplify ((sqrt(640)*5)/(sqrt(8)/((sqrt(4) - sqrt(400)) + sqrt(4) + sqrt(4))))**2.\n | 392000\n | ibivibiv/math_instruct | |
Two letters picked without replacement from nnikkknuuqiiin. What is prob of sequence uu?\n | 1/91\n | ibivibiv/math_instruct | |
Simplify (sqrt(18) - 3*sqrt(72)/sqrt(4))/((sqrt(126)/sqrt(2))/sqrt(7)) + -5.\n | -5 - 2*sqrt(2)\n | ibivibiv/math_instruct | |
b"What is the mth term of 123, 222, 321, 420, 519?\n" | 99*m + 24\n | ibivibiv/math_instruct | |
Suppose 2*b = -b - 3*c + 27, 0 = 4*b + 5*c - 31. Suppose -5*n = -0*n - n. Suppose -32 = -2*u - n*u. What is the smallest common multiple of b and u?\n | 112\n | ibivibiv/math_instruct | |
Collect the terms in -r - 11*r + 17*r - 5*r + 2*r**3.\n | 2*r**3\n | ibivibiv/math_instruct | |
Let g(b) = 13*b**2 + 964*b + 267. Give g(-74).\n | 119\n | ibivibiv/math_instruct | |
What is -1c10141 (base 13) in base 6?\n | -531322552\n | ibivibiv/math_instruct | |
Express 2*o**2 - 13 - 8*o**3 + 21 - 297*o - 2*o**3 + 594*o - 292*o as d*o**2 + l + x*o**3 + b*o and give b.\n | 5\n | ibivibiv/math_instruct | |
Let l(q) be the second derivative of 23/10*q**5 - 29*q**2 + 0*q**3 + 2*q + 26 + 0*q**4. Find the first derivative of l(d) wrt d.\n | 138*d**2\n | ibivibiv/math_instruct | |
What is prob of picking 1 u and 1 c when two letters picked without replacement from uuuucuuoyycucouu?\n | 9/40\n | ibivibiv/math_instruct | |
Collect the terms in -214*d + 865*d - 214*d - 219*d - 197*d.\n | 21*d\n | ibivibiv/math_instruct | |
Let q = 2665/6 + -438. What is the common denominator of q and 75/2?\n | 6\n | ibivibiv/math_instruct | |
Let m = -753 + 1677. List the prime factors of m.\n | 2, 3, 7, 11\n | ibivibiv/math_instruct | |
Let z(d) = -d**3 + 6*d**2 + 7. Let i be z(6). Suppose -2*y + i = -49. Calculate the remainder when y is divided by 0 - (0/(-2) - 15).\n | 13\n | ibivibiv/math_instruct | |
Let w(d) be the first derivative of 0*d**3 + 0*d - 3/2*d**4 - 11/2*d**2 + 3. What is the second derivative of w(u) wrt u?\n | -36*u\n | ibivibiv/math_instruct | |
Suppose -7*y + 499 = -383. What is the highest common factor of 36 and y?\n | 18\n | ibivibiv/math_instruct | |
What is the square root of 158793219 to the nearest integer?\n | 12601\n | ibivibiv/math_instruct | |
Expand 2*m**3 - m**3 - 3*m**3 + (-4 + 3*m + 4)*(-3*m**2 + 3*m**2 + 2*m**2) + 172*m**3 - 58*m - 187*m**3 + 60*m.\n | -11*m**3 + 2*m\n | ibivibiv/math_instruct | |
Let o(l) = 35*l - 5. Let z(t) = -99*t + 14. Let i(c) = -17*o(c) - 6*z(c). Let a(h) = -h + 4. Calculate a(w) - 3*i(w).\n | 2*w + 1\n | ibivibiv/math_instruct | |
Is -10562 smaller than -10562?\n | False\n | ibivibiv/math_instruct | |
What is eleven halves of a millisecond in microseconds?\n | 5500\n | ibivibiv/math_instruct | |
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"# A Banach algebra that cannot be represented on a Hilbert space
Can someone give me an exemple of a Banach Algebra $A$ which does not have an isometric representation on a Hilbert Space? (With a proof or a reference to the ... | To begin, let's define some key terms and establish their relevance. A Banach algebra is an algebra over the complex numbers that is also a Banach space, meaning it has a complete norm and associative multiplication operation satisfying certain conditions. The concept of a *-algebra refers to an algebra equipped with ... | ibivibiv/math_instruct | |
Simplify (((o*o**(-8/9)*o**(1/9)*o)/(o/o**(-2/17)*o**7))**(-2/29))**(1/36) assuming o is positive.\n | o**(1055/79866)\n | ibivibiv/math_instruct | |
Four letters picked without replacement from ffffghfwqwqqxfxffhhf. Give prob of picking 1 q, 1 g, and 2 w.\n | 1/1615\n | ibivibiv/math_instruct | |
-7*-0.158\n | 1.106\n | ibivibiv/math_instruct | |
What is the hundreds digit of 64288135?\n | 1\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {d: 1, r: 2, j: 1, m: 3}. What is prob of sequence jd?\n | 1/42\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {h: 4, c: 2, u: 1, d: 3, j: 2}. Give prob of picking 1 u and 2 j.\n | 1/220\n | ibivibiv/math_instruct | |
Let a(u) = 1305319*u - 1305320*u + 4*u**2 - 1 + 3. Determine a(1).\n | 5\n | ibivibiv/math_instruct | |
Let d be ((-104)/16 - -7)/((-1)/(-2)). Let s be d/(18/132) + 2/(-6). Solve s*i + 10 = 2*i for i.\n | -2\n | ibivibiv/math_instruct | |
Which is smaller: -22 or 1301?\n | -22\n | ibivibiv/math_instruct | |
Is 12 a factor of 1915267648?\n | False\n | ibivibiv/math_instruct | |
Convert -11011100 (base 3) to base 4.\n | -233121\n | ibivibiv/math_instruct | |
Let v(s) = -2 + 3 - 122*s + 118*s. Give v(5).\n | -19\n | ibivibiv/math_instruct | |
What is 79915 to the power of 1/3, to the nearest integer?\n | 43\n | ibivibiv/math_instruct | |
Let 3*d**4/2 - 10365*d**3/2 - 271779*d**2/2 + 908541*d/2 = 0. Calculate d.\n | -29, 0, 3, 3481\n | ibivibiv/math_instruct | |
Does 431 divide 38974468?\n | True\n | ibivibiv/math_instruct | |
b"What is the th term of -1816, -14895, -50502, -119899, -234348, -405111, -643450?\n" | -1877*b**3 - 2*b**2 + 66*b - 3\n | ibivibiv/math_instruct | |
What is the highest common factor of 27 and 65889?\n | 9\n | ibivibiv/math_instruct | |
Is (3/3)/(-1)*-1895 composite?\n | True\n | ibivibiv/math_instruct | |
What is 705 minutes before 1:33 PM?\n | 1:48 AM\n | ibivibiv/math_instruct | |
Let y = 0.22067 + -1.22067. Which is the nearest to y? (a) 9 (b) 0.3 (c) 0 (d) 16/7\n | c\n | ibivibiv/math_instruct | |
Round -1.976 to 2 dps.\n | -1.98\n | ibivibiv/math_instruct | |
Suppose -5*u - 3*l = -0*u + 7, 13 = -3*u - 4*l. Is (-2335)/(2 + u + -4) prime?\n | False\n | ibivibiv/math_instruct | |
b"What is the zth term of -5533, -11067, -16601, -22135?\n" | -5534*z + 1\n | ibivibiv/math_instruct | |
Is 9049108403 a prime number?\n | False\n | ibivibiv/math_instruct | |
Solve -162*w + 25170 = -169*w - 1671*w for w.\n | -15\n | ibivibiv/math_instruct | |
Which is smaller: 245 or 244?\n | 244\n | ibivibiv/math_instruct | |
What is -6258700 rounded to the nearest 10000?\n | -6260000\n | ibivibiv/math_instruct | |
Does 94 divide 94582612?\n | True\n | ibivibiv/math_instruct | |
What is 332 (base 4) in base 5?\n | 222\n | ibivibiv/math_instruct | |
Which is the fourth biggest value? (a) -92 (b) -1/10 (c) -3 (d) -2\n | a\n | ibivibiv/math_instruct | |
Let b(u) = u**2 - 24*u. Let j be b(24). Let o(y) = -y**2 - 2*y + 1. Let x be o(j). Solve 2*t = -x - 3 for t.\n | -2\n | ibivibiv/math_instruct | |
Let n(u) = 18*u - 3. Let q be 0/126*2/4. Determine n(q).\n | -3\n | ibivibiv/math_instruct | |
Let n(o) = -13*o**2 - 96*o + 624. Give n(4).\n | 32\n | ibivibiv/math_instruct | |
Let l = -2 - -3. Let g = l + -0.88. Let q = g + -5.12. What is the closest to 2/5 in 4, q, 1?\n | 1\n | ibivibiv/math_instruct | |
Four letters picked without replacement from {v: 1, b: 18}. What is prob of picking 3 b and 1 v?\n | 4/19\n | ibivibiv/math_instruct | |
Simplify (-6*(sqrt(1088)*-6 - 1*sqrt(1088)))**2.\n | 1919232\n | ibivibiv/math_instruct | |
Let s(l) = -4*l**2 + 24*l - 20. Let o(k) = -k + 1. Let m = -23 + 22. Let z(w) = m*s(w) - 12*o(w). Determine b, given that z(b) = 0.\n | 1, 2\n | ibivibiv/math_instruct | |
What are the prime factors of 1886?\n | 2, 23, 41\n | ibivibiv/math_instruct | |
Let p be -1*((-1)/(-2) - 1). Let b be -1*(35/(-30) - (-10)/15). Find u, given that 0*u - 1/2*u**4 + 0 + p*u**2 - 1/2*u**3 + b*u**5 = 0.\n | -1, 0, 1\n | ibivibiv/math_instruct | |
Calculate the common denominator of 29/8784 and 65/15372.\n | 61488\n | ibivibiv/math_instruct | |
Let f(q) be the second derivative of 2*q**5/5 - 2*q**3 - q. Find the second derivative of f(i) wrt i.\n | 48*i\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 l, 2 u, and 1 b when four letters picked without replacement from pllpluplblllcpp.\n | 0\n | ibivibiv/math_instruct | |
Let -8*l**4/3 + 9598*l**3/3 + 7208*l**2 + 14422*l/3 + 2404/3 = 0. Calculate l.\n | -1, -1/4, 1202\n | ibivibiv/math_instruct | |
Suppose -11*q + 13 = -9. Find the third derivative of 28 - 28 + 226*y**3 + 45*y**q - 99*y**2 + 19*y + 53*y**2 wrt y.\n | 1356\n | ibivibiv/math_instruct | |
Which is smaller: -12 or -73/6?\n | -73/6\n | ibivibiv/math_instruct | |
Solve -89*r + 4*g - 12 = -27*r - 30*r - 32*r, -2*g + 4*g = -9*r + 195 for r.\n | 21\n | ibivibiv/math_instruct | |
Express 5*f + 6*f - 97*f as k*f + o and give o.\n | 0\n | ibivibiv/math_instruct | |
Suppose 5*b = -5*m - 20, -m - 6 = -3*m. Let f = 26 + b. Suppose 6*g = -1 + f. Solve g*u = -y - 0*u - 10, -u = 3*y + 6 for y.\n | -1\n | ibivibiv/math_instruct | |
Let i = 431 + -431. Suppose z - 13 = -5. Suppose -f = 4*u - 0*f - z, 6 = 3*u + 3*f. Solve 4*l - 18 + u = i for l.\n | 4\n | ibivibiv/math_instruct | |
b"What is the rth term of 11, 6, 1?\n" | -5*r + 16\n | ibivibiv/math_instruct | |
Let d(c) = -c**3 + 6*c**2 - 2*c + 14. Let m be d(6). Let n be 32 - ((-3)/m)/((-2)/4). Round n to the nearest ten.\n | 30\n | ibivibiv/math_instruct | |
Let r(a) = -6*a**3 - 114*a**2 - 150*a - 2844. Determine r(-19).\n | 6\n | ibivibiv/math_instruct | |
Let r = -14.4 - -14. Let l = 0.2 + r. Which is greater: -12 or l?\n | l\n | ibivibiv/math_instruct | |
Solve -4037*s + p = -4041*s + 14, p = -3*s + 19 for s.\n | -5\n | ibivibiv/math_instruct | |
Suppose 0*v - 3*v + 30 = 0. Let g be 4/v + (-2827)/7205. Let z = 921/524 - g. Which is the second biggest value? (a) 0 (b) z (c) -2/9\n | a\n | ibivibiv/math_instruct | |
What is -b54739 (base 13) in base 11?\n | -24343a1\n | ibivibiv/math_instruct | |
Let m = 22 - 5. Calculate the greatest common divisor of 17 and m.\n | 17\n | ibivibiv/math_instruct | |
Suppose -v = -4*o - 4*v + 1, 2*o = 5*v - 19. Let f be -4*((-62)/8 - o). Let p = f - 5. Calculate the lowest common multiple of 22 and p.\n | 198\n | ibivibiv/math_instruct | |
Let u(s) be the second derivative of s**5/20 + 2*s**4/3 + 7*s**3/6 + s**2 + 4*s. Let y be u(-7). Let j = 6/359 + 323/2154. Put -3/2, y, j in decreasing order.\n | y, j, -3/2\n | ibivibiv/math_instruct |
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