Compute complex math (integration, derivation,...) [closed]

How can I compute complex math in a programming language like:

integration
derivation
some other non-trivial math

For example for these languages:

Java
Ruby on Rails

I know that for C# exists Math.NET, but for the others?

What is closed contour in complex analysis?

A contour is a piecewise smooth curve. That is, z(t) is continuous but z (t) is only piecewise continuous. If z(a) = z(b) then it is called a simple closed contour. Contours are important because they are the sets that complex integration, or integration of complex functions of a complex variable, are defined on.

I don't know about Ruby, but for math in my Java applications I've used Apache Commons Math. It provides a number of reusable components for probability, statistics, linear algebra, and numerical calculus.