Essentially, I mean all kind of calculations which can be done with the xtensor pacakage of xact on Mathematica. (Personally, I don't like Mathematics for various reasons, two being lack of control and representation, and  I didn't know xact until a few days ago). 

A trivial example would be to derive the connection between the curvature of the Levi-Civita-connection of a metric and the curvature of a corresponding metric obtained by a Weyl transformation,i.e. a conformally equivalent metric, or to check Weyl/conformal invariance of the sacalar field in arbitrary dimensions. These calculations are tedious, but still possible by hand, but I have no idea how to do this in Maple. More advanced applications would be e.g. to check some formulas in AdS/CFT. 

The most critical restriction is not the dimension, but the need to have a concrete defined metric, since otherwise the default Minkowski applies. Metric "arbitrary" is not an option, since it gets unuseable slow and cluttered already for 8 dimensions i(dn't try 6 or 7, maybe even there) - so definitely not useable for calculations in string or M-theory or gravity in 10 or 11 dimensions.  

Since there seems to be no solution, I'm afraid I have to learn xact on Mathematica.. I really like the physics package in Maple, it is excellent for many purposes, unfortunately not for me at the moment...