Simpson's rule to calculate integrals in Felix. (Very similar to Scala version: http://gist.github.com/gbluma/5140262 )

Simpson.flx

/** Using   Simpson's rule to calculate integrals in Felix
 *  Date:   March 11, 2013
 *  Author: Garrett Bluma
 

 h/3 (y_0 + 4y_1 + 2y_2 + 4y_3 + 2y_4 + ... + 2y_{n-2} + 4y_{n-1} + y_n)

 where h = (b - a)/n for some even integer n
 y_k = f(a + kh)
 increasing n increases accuracy

*/

open System;

fun sum(term:double->double, a:double, next:double->double, b:double):double =>
    if (a > b) 
      then 0.0
      else term(a) + sum(term, next(a), next, b);

fun cube(a:double):double => a*a*a;

fun y(f:double->double,a:double,h:double)(k:double):double => f(a + k*h);
fun next_n(n:double):double => n + 2.0;
fun simpson( f:double->double, a:double, b:double, n:double):double = {
  val h = (b - a)/n;
  return (h / 3.0) * ( y(f,a,h)(0.0)
                     + y(f,a,h)(n)
                     + (4.0 * sum( y(f,a,h), 1.0, next_n, (n - 1.0)))
                     + (2.0 * sum( y(f,a,h), 2.0, next_n, (n - 2.0))));
}

println$ simpson( cube, 0.0, 1.0, 2.0 );
// => 0.25