@Carl Love : Your posts are always informative. However, I did not ask maple to calculate N^(1/3) for an extremely large integer, I asked Maple to find 8^(1/3), and it failed. In Mathematica, I set n = 10^1002, asked for n^(1/3), and Mathematica returned a very large power of 10. It took no time at all. I did not count the digits, but I would bet my left arm the answer is correct. Score one for Mathematica.
Also, for real N, if no other context is given, N^(2/3) is by definition the square of the real cube root of N, so I'm not sure why Maple forces you to use "surd" if you want to find N^(2/3). With my n=10^1002 from above, Mathematica also found n^(2/3) instantly, so there is probably a way the maplesoft people can fix this behavior.
Perhaps Maple should test if a quantity is likely to have a simple cube root and if so, compute it, rather than failing on extremely easy problems.
I don't understand why Maple and Mathematica both fail to graph x^(2/3) correctly. Every good calc student knows how to graph that. If you are plotting a function of a real variable in the Cartesian plane, you don't mess with complex numbers at all unless you have a good reason. For real x, x^(2/3) is the square of the real cube root of x. One could provide excuses for both Maple and Mathematica, but the fact is, Maple and Mathematica are producing incorrect graphs. I think both languages are supposed to be easy for people to use, and not optimized so computers can use them (which might be at least partially true for C/C++, for example).
If Maple can do sophisticated mathematics correctly, it should be able to do basic mathematics correctly. A student or professor should be able to plot x^(2/3) in Maple without messing with initialization files or using additional commands.
I have never edited an initialization file, and I would bet that a tiny fraction of Maple users have. One cannot expect students to do it on their own computers (you can't even expect them to change Maple's newer default settings to better ones). If one uses Maple on multiple classroom computers, it may be impractical. If one is using Maple installed on a central server, it may be difficult or impossible without assistance from one's IT department.
I like Maple, and I prefer it to Mathematica, but I won't let brand loyalty prevent me from complaining about what seem to me to be obvious flaws, and seeking solutions.