Integral of function f(x) in the interval (a,b) is computed using Simpson's rule by the `integral' statement of the form <variable>=integral(f(x))from(a)to(b) or in extended forms <variable>=integral(f(x))from(a)to(b)eps(eps) , <variable>=integral(f(x))from(a)to(b)eps(eps)n(n) . The original range (a,b) is split by 2^n equidistant points using n=1,2,3,... until the relative error is <eps or the optional n value is achieved. Default values are eps=1e-10, n=12. Examples: ................................................................................ a=0 b=1 eps=0.0001 pi=3.141592653589793 infinity=10 I1=integral(x^2)from(a)to(b)eps(eps) I2=integral(exp(-x*x/2)/sqrt(2*pi))from(-infinity)to(0) I1.=0.33333333333333 I2.=0.5 ................................................................................ Number of prime integers less than N ( here N=1000000 ) can be roughly approximated by the integral integral(1/log(x))from(2)to(N)eps(0)n(17)=78627.636537002 while the true number is 78498. E = More information on editorial computing