Just to chime in, as someone who has dealt with this question a lot 
(though, perhaps ironically, never in a classroom situation):
I would be very against a "cuberoot" function, but an "nthroot" function 
where it was really clear what input was allowed could fly.  I appreciate 
Greg's rationale.  Note however - what is the 0.1 power? Is that the same 
as the 1/10 power?  This is a tricky floating point question to interpret. 

I don't think that the slowdown would be too bad since it would primarily 
be for pedagogical purposes for plotting.

David, I don't know how this would work with integrals, though - we'd have 
to see if Maxima had something equivalent.  Perhaps it could do a temporary 
set of the Maxima domain to real somehow, if that is what allows Maxima to 
do the "right thing" in this context, I don't know.

Thanks for fighting the good fight on trying to resolve this once and for 
all!
- kcrisman

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