Math-engines, Mathematica, Maple or ...

I'm working on a system, that involves a browser-based frontend with 
mathematics support.
I would like to make it possible to use mathematic-engines like 
Mathematica, but their license restrictions are very strict, so I'm trying 
to figure out what engines that there is out there.

The engine must be able to:
    * Do symbolic calculations
    * Make plots
    * Do numerical calculations

The license restrictions must make it possible to do some calculations over 
the internet.

What engines are there, how good are they and how strict are their license 
policies?

Is there some open-source projects..?

Regards

Morten Andersen