Mac function graphing?

A teacher is having us type out mathematical proofs. She wants us to include graphs in our proofs. The graphing program she wants us to use is windows only (a basic freeware graphing program). I have a mac.

I’m looking for the most fully functional graphing program for the mac (preferably freeware) available. It should be able to graph polar functions alongside cartesian functions. Tools that calculate differentials and integrals would also be helpful.

I know about mathematica, but I don’t have it and probably can’t get it legally.