Addi

Much more than a scientific calculator.
A Computing Environment useful for solving many complex problems.
A Matlab / Octave clone for Android.
Java based and open source.
Free and Ad free.
Has most needed math capabilities.
A lot of function included already.
Can parse and run .m files. (try "edit /sdcard/test.m")
Working on bugs and compatibility.
Basic plotting working (you need the app called AddiPlot).
Custom keyboard for entering commands faster.
http://addi.googlecode.com

Now have Octave built for Android, moving this soon to a separate app called "octave" (clever...I know). You can go checkout the first version soon. Addi will be going back to being solely java based and small and not very feature rich, while octave will be the real deal, but much larger.

Matlab is a registered trademark or Math Works.