@tomleslie Thanks for posting the details. I now feel a bit embarrased that I misunderstood when @Carl Love 11625  said 'simplify(m) on nested piecewise'. Thank you all!

@Carl Love Yes I did, but maybe I misunderstood you? Could you please attach your mw or PDF? Thanks,

@tomleslie m defined by this approach gives an ugly print output of m. And I would prefer a 'beautiful' m printed by print command... :)

@Carl Love In my mw, I wanted to show that m defined by these two methods are not idea, I don't want to define m piece by piece...

@Carl Love Not sure if I get what you mean...

@Kitonum Thanks a lot for trying. However, the solution m(p) can't be shown as normal piecewise function. It is not only for plot, because I can restrict p=1..9 in a plot. It is really for 'print'...

@Mariusz Iwaniuk That's very nice of you to have shared this solution.

The crashes caused a loss of 1/3 of my thesis yesterday (recovered from latest backup so only ~4h of rework required).

Anyways, I will upgrade to the latest Maple version as soon as possible.

@vv This is indeed how I used convert/float for. But the system (windows 10) still crashes...

@brian bovril Exactly!!! DirectSearch is the perfect solution!!!

@Mariusz Iwaniuk the numeric helps a little, but not too much. Converting f to heaviside doesn't help much with the real piecewise functions. Maple crashed my laptop four times while running the int/evalf.

I suppose the real issue is the second function with ln and epsilon. When I do below, it runs a bit faster:

int(convert(abs(fl33_1-q_1), float), p = 1 .. 9, numeric)

@Carl Love This is exactly what I am looking for, the 'parse' command. Thank you so much!!!

@tomleslie I know this approach :)

But I want to find the absolute maximum value throughout the whole interval. Fsolve only finds the local maximum. It doesn't fit in a procedure. @Joe Riel 6935 's answer fits perfectly in this context. Thank you both.

@Preben Alsholm Thanks for checking, I want to write this in a procedure, that's why a guess doesn't treat for all situations.

I already know it by using op(). Thanks all for viewing anyways

I tried both and both works as required! Can't thank you enough!