Sage is a free, open-source computational mathematics system in the vein of things like Mathematica and Maple. For the past few years, there’s been an online version called the Sage Notebook which worked pretty well, but it was pretty slow and not particularly easy to use.
Now the creator of Sage, William Stein, has started work on The Sagemath Cloud. It’s considerably more ambitious than Sage notebook – as well as the Sage notebook interface, it gives you a sophisticated area where you can write LaTeX files with live preview, work on IPython notebooks, and even bring up a Unix terminal to do the kinds of things you need a Unix terminal for.