I'm not a expert on programs available so it would be useful if you could provide with a list of useful program which can be used at degree level.
Otherwise, I know Maxima, which is quite alike, and free.
In both cases, you have to learn the syntax, what to type, etc... This is, imho, the most delightful (irony) part of these programs ^^
Concerning geometry you can use Geogebra. I can't tell much about it because I installed it only few weeks ago. But it's used in some high schools in France (if you want a reference).
Google will give you the links =)
Hope it helps.
Yeah, here also taught me to use Maple.
As for geometry, you could try CorelDraw, it's amazing, I used to make geometric pics and the quality is just excellent.
MathType for LaTeX typesetting or Texaide. (First one is posted by me, look at my threads if you want to give it a try.)