Maple implicit assumption is that the numbers are complex, for which your formula does not hold in general. E.g.:

K^(p-1)*L^(-p+1)=(K/L)^(p-1):
eval(%,[K=-I,L=I,p=1/2]):
evalf(%);
                      0. + 1.000000000 I = -1. I

So, you have to tell Maple explicitly about the implicit assumptions used in your hand calculations.

I would find fit that you start a new blog where contributions for answering Paul's question What significant enhancement or new feature of Maple would you like to see in Maple 15? could be added.

I have many requests. Not eye catching, but mainly about the mathematical foundations in Maple, which I do not find so solid.

There could be problems with banning these domains. For instance, about two years ago I had to switch to a gmail address in my MaplePrimes account as email notifications never reached to my university address (I could not get any information about the cause of this problem).

There could be problems with banning these domains. For instance, about two years ago I had to switch to a gmail address in my MaplePrimes account as email notifications never reached to my university address (I could not get any information about the cause of this problem).

I have repeated the same test, this time in Maple V Release 5.1 (1998, pre Java era). I.e. same platform as I have mentioned above and same random key pressing at my maximum speed. I get a CPU usage not over 8%. Same result with Georgios method (keeping pressed a single key).

On the other hand, in Maple 13.02 Standard and 2D input, I can get close to 50% of CPU usage by random key pressing. Clearly because of the way some keys get parsed. 

Indeed, my test was not with "real typing" but pressing whatever keys as fast as I can. But I know that other persons can move their fingers much faster than me!

Yes, I think that 15-20% is a bit on too much, but actually I have not made the same test in the GUI of some other program to make a sensible comparison.

For sure, my expectation was that Standard GUI would use more CPU than Classic. But I have repeated this test several times (until my fingers got tired) and found the reported figures quite reproducible.

Before taking such drastic mesures as wiping a drive I would investigate a bit more on the OS side, as Maple is not accessing the keyboard directly but by an OS driver. I.e. it might be a driver/configuration issue.

Later I will boot into Linux and make the test again.

Yes, this help page is far from useful about the methods implemented. Some developers, held the position that avoiding details is good (I think that I cannot reproduce here the sources). 

I am not aware of a post about summing the last weeks, but this thread could be somewhat useful.

In a quite similar machine: P4 3 Ghz with 2 GB RAM, under Win XP 32 bit, I can get in maple 13.02 Standard GUI up to 15% of CPU usage, while in Classic it may reach about 20%. But my maximum typing speed may be slower than yours...

There are some paragraphs on _EnvFormal at the end of ?sum,details  > Details, but they are too vague for my taste.

If only a few of these 600, say 20, are intended for the user, it would be not much work to write their list, isn't it?

I have quoted the expression, following the sense given to it by Pagan above: program analysis, DSLs, etc.

As an outsider to this subject, I wonder: are these "sophisticated coding techniques" being used in other CAS?

You are not the first one requesting it. Do a search for "abstract linear algebra".

Symbols as implicitly assumed complex, hence the transformation may not hold:

ex:=x^(3/5)*y^(4/5):
combine(ex,radical) assuming real;
                               3  4 (1/5)
                             (x  y )

Symbols as implicitly assumed complex, hence the transformation may not hold:

ex:=x^(3/5)*y^(4/5):
combine(ex,radical) assuming real;
                               3  4 (1/5)
                             (x  y )