@J F Ogilvie Googling "define: kid" and scanning the first full page of hits, I find not a single dictionary that marks its definition "human child" as crude (or equivalents such as "offensive", etc.), American, or slang. All classify it as "informal". All except one list this as its first definition. The oldest known usage of this definition is from the 1590s, and it hasn't been considered slang since the 1840s.

Unless theta, q, b, and w have some especially simple form, I'm very doubtful that it's mathematically possible to maximize with symbolic sP and sL.

@michele There is a bad habit among newbies to load unnecessary packages in every worksheet, especially plots and LinearAlgebra.

@emendes Commands, such as coeffs, that return values by modifying their arguments are an unfortunate relic of ancient Maple. It's unfortunate for two reasons:

1. It's considered a bad programming practice in any language.
2. Specifically in Maple, it's impossible for a superficial syntax checker to know whether 'M' means a name through which a value will be returned, and thus should probably be local, or a keyword argument, and thus must be global. So, this is why you unfortunately got no warning about this.

To avoid this and other awkwardness with coeffs, I almost always use it with this wrapper:

Coeffs:= (p, v)-> local M, C:= coeffs(p, v, M); table([M]=~[C]): 

Then after T:= Coeffs(p, v), if only the mononials are wanted, they can be extracted as indices(T, nolist).

@max125 It's instantaneous for me also:

CodeTools:-Usage(plot(sin(t/100), t= 0..1000));
memory used=415.18KiB, alloc change=0 bytes, cpu time=0ns, real time=10.00ms, gc time=0ns

If it's not instantaneous for you, try it in a fresh worksheet.
 

@max125 Yes, by using modp, as in this minor update to John Fredsted's procedure:

expMod := proc(pol::polynom(integer,x),p::prime)
   modp(map(y -> lcoeff(y)*x^(ldegree(y) mod p),pol), p):
end proc:

The p in modp stands for positive.

Your pi(tau) is an unknown function of tau. How can it be possible to solve for tau an equation that contains an unknown function of tau? The only thing that remove_RootOf does in this case is return your original equation. RootOf is just Maple's way of expressing inverse functions. It always uses _Z as its bound variable.

@nm You made a very valuable comment about StackExchange, and I was just about to respond to it, yet now you've deleted it! Please stop doing that!

Unless there's just by chance some physicist reading this who has the specialized knowledge required, the only way that you're going to get any help here is by posting your failed attempts. If the failure is due to a lack of understanding of Maple, it's very likely that we can help. If it's due to something else, it's much less likely.

@DJJerome1976 It is very difficult to program a command to make use of assumptions. The only ones that solve can handle are directional inequalities. The help page that acer linked implies that in the case of directional inequalities, the useassumptions option is equivalent to the method that I showed.

@nm Please stop deleting your Answers! You do this very often. In this case, there was nothing wrong with your Answer. It did the same thing as my Answer in a different way. It's likely that for some readers your way would be more understandable than my way, or that the combination of Answers would reinforce the learning.

@DJJerome1976 The lprint is not needed to do the job; it's merely there to help you understand the next line of code. That next line of code will work in all cases; it's not specific to your case.

It's despicable that you've deleted your Question after one of our volunteer experts went through the trouble of answering it for you. And to top it off, you've left this ugly and meaningless name "1111..." in our index.

@MapleEnthusiast I've been following that other thread. Unfortunately, I don't have any constructive input at this time.

@michele The symbol interactive has no predefined value when a Maple session is started. That changes when you use with(plots) because the plots package has an interactive command. So, when you use the symbol interactive for DrawGraph, you need remove any value that it has acquired. Prefixing any symbol with : - means that the reference is to the global symbol rather than to any package's symbol. Enclosing it in single forward quotes means to ignore any value that has been assigned to the symbol.