You may want to look into the Sage software (python distribution of 
scientific libraries and python goodies + a consistent interface), 
specifically the "interact" feature:

http://interact.sagemath.org/
http://wiki.sagemath.org/interact

the "sage cell server":

https://sagecell.sagemath.org/static/about.html?v=15adefe8b7e89fcf49eda7af5303abd4

and the Sage Cloud:

https://cloud.sagemath.com/

Your work could be simply to create one Sage interact like the many 
examples you can see above for any calculator you want to offer, and then 
offer the interacts to visitors. Once the structure is set, it would take 
very little effort to add new calculators (work in a local sage install to 
get the interact, then login as admin and upload the interact to the 
server).

Sage includes scientific software for almost any task, it's incredibly 
simple to add cython snippets to boost performance of critical parts of the 
code, the community is super-friendly (try sage-support, sage-devel, and/or 
ask.sagemath.org), and everything is open source. They even offer private 
sage cell clouds, so that they would do all the computation in their 
servers.

-- 
Resources:
- http://web2py.com
- http://web2py.com/book (Documentation)
- http://github.com/web2py/web2py (Source code)
- https://code.google.com/p/web2py/issues/list (Report Issues)
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