Using Simpson's rule to calculate integrals in Scala.

Simpson.scala

/** Desc:   Using Simpson's rule to calculate integrals in Scala. 
 *  Date:   March 11, 2013
 *  Author: Garrett Bluma
 */
object Simpson
{

  def sum(term:Double=>Double, a:Double, next:Double=>Double, b:Double):Double =
    if (a > b) 0.0
      else     term(a) + sum(term, next(a), next, b);

  def cube(a:Double):Double = a*a*a;

  def simpson( f:Double=>Double, a:Double, b:Double, n:Double):Double = {

    def y(f:Double=>Double,a:Double,h:Double)(k:Double):Double = f(a + k*h)
    def next_n(n:Double):Double = n + 2.0

    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))))
  }

  def main(args:Array[String]) {
    println( simpson( cube, 0.0, 1.0, 2.0 ) )
    // => 0.25
  }
}