@Carl Love You wrote  "Because the module references are linked into the code at the time that the code is read, not the time that it's executed".

But when uses IM is parsed, IM was already parsed, so the exports are known and it would be enough for the parser to "observe" that add_three is exported by IM and to add the IM:- prefix.
I don't see any reason to reject uses IM.

@mmcdara 

1. I think that this can be set with the Typesetting package, e.g. with the interactive Typesetting[RuleAssistant]()
I do not use it much. Anyway, after with(Logic) the desired typesetting is automatic.

2. A name beginning with & is treated as a binary operator (or prefix unary). See ?neutral operators

@greatpet I don't know why uses does not work in this form. But it does with "equations" (which is actually more clear and allows abbreviations):

restart;
OM := module()
option packge;
export IM:= module()
    option package;
    export add_three := x-> x+3;
    end module;
export times_two_add_three:= 
  proc(x)
    uses k=IM;
    k:-add_three(2*x);
  end;
end module:
OM:-times_two_add_three(z);

@greatpet with cannot be used inside modules and procs. Use the uses clause instead.

@greatpet You may simply write

export procedure1 := IM1:-procedure1;
etc.

E.g. in Carl's example:

restart;
OM:= module()
option package;
export
    IM:= module()
    option package;
    export add_three:= x-> x+3;
    end module;
export add_three:=IM:-add_three;
end module:

with(OM);
#                        [IM, add_three]

add_three(z);
#                             z + 3

@mmcdara Yes, I wanted minimal modifications of the previous answer (for ratpoly).
The unpleasant fact is that solve finds only the solutions with c=0.

@tomleslie Actually I was aware that Excel throws an error for x*m<0 but I don't understand why and I have preferred the simplicity. After all, we may say: Excel is unable to compute MROUND(x,m) when x*m<0.

@mmcdara Merci. For my native Romanian the term is perfect :-)

I am not sure whether this is the right forum for such questions. Better choices could be https://math.stackexchange.com or https://mathoverflow.net. A CAS cannot help much when a proof needs more or less special theorems/formulae to be applied. For example, Maple cannot manage the limit of a sequence: limit(h(n), n = infinity) assuming n::even.

@Guy1  The idea is to avoid Maple's light, ambientlight or lightmodel, and use color as in my example. E.g. to change the direction of light, just change light:=[-1/sqrt(3),-1/sqrt(3),1/sqrt(3)].
For a secondary light source, take two lists light1 and ligt2 and combine them. There are many computer graphics methods, but probably Maple is not the best tool for such effects.

@Lynge Jensen
OK, but Maple does not know about turbineblades and your assumptions. 

int((x+1)^2, x) = int(x^2 + 2*x + 1, x);

@Kitonum You took another expression instead of  ln(piecewise(t = 0, 2, 0 < t, 2 + 5*t)).
Yours is simply ln(2 + 5*t)

@Carl Love You are right about  Gershgorin ==> spectral radius(stochastic) <= 1. I was fooled by the standard proof.

The OP's M seems however to have r=1.

@MapleEnthusiast 
1. The "how" answer is useless. What linear system?
Suppose e.g. that we start with a stochastic matrix S having some symbolic elements. If P is an arbitrary nonsingular matrix also with some symbolic elements then P^(-1).S.P has the spectral radius <= 1 but it will be very hard to prove it without knowing S and P.

2. A Neumann series ( = Sum(A^k, k=0..infinity)) cannot converge if A's spectral radius is >= 1.

@MapleEnthusiast The Gershgorin theorem is too simple to hope for a proof. It is useless even to prove the result for standard stochastic matrices. It would be more important to explain how (and why) the matrix M was obtained.