You can try DERIVE ... it was already good at the time, but now I think it can be better.
It is much more simple to use than Mathcad or Matlab... You can find a student version or trial version, if I remember correctly.
In the "old days", Maple had a rather cumbersome notation for symbolic-anything. I've always used it as-bundled with MathCAD, yielding human-readable formulae. I would HOPE Maple learned from this.
Much time has passed between then and now.
Be sure to check for this - it is crucial, though I would be quite surprised if they have not modernized their look and feel to the point of being readily useful.