Hm ... it is not clear for me what you actually want ... a language problem?
I have not cared for .Net so far and actually it should not matter (you will
have to take care for such things through coding).
Anyway: usually I start from Maple and call something external (a library)
and never tried it the other way round (except call backs for integration,
but that's a 'trivial' thing).
What do you actual want?

That is only true if A is an invertible matrix: then you have exactly 1 point
as solution. That already enforces A to be a square matrix.
However much (I would say: almost all) stuff in linear Algebra is about the
more general situation when A is neither a square nor has maximal rank.
In that case the solution is an affine linear subspace (for example a line or
a surface). All the things around solving linear equation are devoted to that.
May be you want to look up in some book about linear Algebra ...
The main difference between your first example and the desired feature is:
x+z+1=0 is an equation in the additive group (where the word group already
implies that any element has an inverse, in that notation a commutative
group is supposed).
A*x-b=0 involves 2 different 'structures' and multiplication is neither a
'commutative' thing nor one has inverses.
If you type solve(A*x=b,x) into a fresh Maple sheet it responds by b/A which
is b*A^(-1) just in a different notation.
However it is not quite correct (it implicitely says: if A is invertible and
some commutation, which is not obvious), but ok for me (I never checked what
Maple actually assumes as math structure when not given an explicite one).
However it would not make much sense to do so if A is explicitely thought as
a matrix.

It does mot work because that is generally not correct, theta in
1/2 + Z*Pi gives a tan of +- infinity.
arctan(sin(x)/cos(x)): pb:=convert(%,tan);
sin(x)
arctan(------)
cos(x)
simplify(pb);
arctan(tan(x))
simplify(pb) assuming ( -Pi/2 LT x and x LT Pi/2);
x

Edited: grrr, Alec was faster ...

Certainly I am not a good coder - but I would avoid to use lists here,
especially for list of strings. May be the easiest is to wrap your fct
in Maple to one with 6 arguments. Then you just use the conversion from
C format to Maple format. Do not forget: it is a C interface, not C++,
so you have to care for your string arguments. The best thing is to go
through the examples, which come with Maple (actually I would avoid the
strings if possible and use integers to code the color names, wrap them
in Maple).

googling old threads in the usenet I found "problem
reading complex integer numbers" from 2002, where
Robert Israel points to restricted nature of the
command.
However here the following should do:
pp:=proc(str)
StringTools[SubstituteAll](str," ","");
StringTools[SubstituteAll](%,".E",".0E");
parse(%);
end proc;
PS: the box for entering contributions here is much
to small

if i call your set of unknowns by unk, then there are 22, yes.
but indets(eqns,atomic): indets(%): % minus unk; nops(%); shows
{s1, s2, v0, s0, vQX, vQY, v1, v2, RT1_FR, RT2_FR, RL1_LS, RL2_LS, PaQv}
so your input produces 13 new variables ... what is s1, s2 etc?
May be a careful input may solve your problem?

That would be fine ... but they would have done, if they think it time
to release it.
And it might not help you - why 50 digits (I think Bailey has special
software for quadrature of high precision)? Plotting shows the problem
is at the boundary.
Some thoughts ... as you do not state all you know for your special
case and I see
- 2 variables (could there be more? - that may be a show stopper)
- coeffs sum to 0 in (x,y)=(0,0), so re-scaling possible?
- there is only 1 mixed term
- staring at the powers: one can reduce to degree 2
Int(Int(sqrt(R)/xi^(99/100)/eta^(1410/1411),xi = 0 .. bX^100),
eta = 0 .. bY^1411)/176375000 where bX, bY are the bounds and
R:=1562500+7582500*eta+9199089*xi^2+7582500*xi+9199089*eta^2
-33563178*xi*eta
Then the problems for the integrator are at 0. Note that order of
integration numerical could make a difference, if the powers are
of different size (as in your case, bounds^m --> 0 with m large)
and one of the bounds is not very close to 1.
Now i looked in Gradsteyn et al ... 2.260.1 has a recursive formula
for Int( x^m * srqt(R), x). One might try to write the denominators
as Taylor series (may be after xi -> 1 - mu etc) and try to write
down a recursion, so the problem becomes an infinite series in
applying the outer integration numerical (plus some stopping, I do
not have a good feeling for convergence rates ...).
But for higher dimension this approach will be quite hopeless and
it reminds me a bit to calculate a (bi-variate) cumulative normal
where correlations ~ +-1 cause problems, but can be settled in the
2 dim case (only) by recursive computations.
But it's just an idea, not a solution.

you just type the formulae in a sheet ...
and for all software new to you: contact the manual for first steps ...
sounds sarcastic, I know, but either i do not understand your question ... or you have not looked into the manual or the only help (just mark in with the mouse and hit F1 key

could you say what you want to do exactly?

There is the possibility to tell Maple to use a default type for the variables.
The other - quite lame - thing I sometimes do is to work with an editor or just
Win Word (which often is easier than to look up commands, especially if one wants
arrays in readable form or other formatings): copy your definitions to the editor
and replace "t" by "float t" using the editor's ability.
But the proper way is to look at some of the examples at the online help.

This is not a function of P_m, since that is your integration variable. If the others are constant that is a real number (or undefined) and I doubt that Maple plots it - what is your input for that?

Even if I accept licence checking as a good thing that is either
an unacceptable behaviour or a bonelazy answer you got. Or both.
Of course I have files which are created in future ... I do not
use my PC for Maple alone.

It is not quite clear for me which constants you use and it may be you cut off
to early (where the exp term is still contributing), but I would do it this way:
Your integral writes as Int(erfc(b*sqrt(xi/(xi+1))) *exp(-a*xi)*a,xi=0..infinity)
for b = B^2, a = 1/gamav.
Here xi/(xi+1) approaches 1 from below for large xi and beyond xi = 1/epsilon-1
differs at most by epsilon from 1. Then split the integration at this point into
Int(a*erfc(b*(xi/(xi+1))^(1/2))*exp(-a*xi),xi = 0 .. 1/epsilon-1) +
Int(a*erfc(b)*exp(-a*xi),xi = 1/epsilon-1 .. infinity);
The last is erfc(b)*exp(-a*(1/epsilon-1)) and the first should be done by working
numerical.
May be you refine that suggestion.

since nobody answers: you may add your hardware and operating system
and may be graphical interface (and personally i just would reinstall
instead of doing anything else ... and de-install first ... and if
you do it try to avoid the blank in the directory name, overwrite it
by Maple10 or similar within the installation dialog ... and if you
have and old OS like WinME - do not use the standard interface)