You can do this
restart:
with(LinearAlgebra):
M:=Matrix([[ 1 , 2 , 3 , 4 ], [ 5 , 6 , 7 , 8 ]]);
b:=Vector[column]([ 10 , 10 ]);
LinearSolve(M,b);
If you prefer x as the free variable name
LinearSolve(M,b, free='x');
See the help page for LinearSolve since there are many options that can be specified. Hope this helps.
Thomas

From the help page solve,details
In the solution, Maple may generate variables that take numeric values. Normally such variables are named with the prefix _Z for integer values, _NN for non-negative integer values, and _B for binary values (0 and 1).
Search help for "solve,details" or enter ?solve,details in your worksheet.
Hope this helps,
Thomas

Here are some ways to get information about your solutions. BTW 0 is not an element of the solution set. It was included in your post above. Neither your TI calc nor Maple seem to eliminate it.
restart:
_EnvAllSolutions:=true:
h:=sin(x)^2/x;
h := sin(x)^2/x
S:=[solve([h=0, x<>0], x)];
S := [{x = Pi*(2*_Z1+_B1)}, {x = Pi*(2*_Z1+_B1)}]
getassumptions(S);
{Pi::Pi, _B1::(OrProp(0, 1)), _Z1::integer}
about(_Z1);
Originally _Z1, renamed _Z1~:
is assumed to be: integer
about(_B1);
Originally _B1, renamed _B1~:
is assumed to be: OrProp(0,1)
Sometimes it is useful to convert trig functions to exponential.
g:=convert(h,exp);
g := -(1/4)*(exp(I*x)-exp(-I*x))^2/x
solve([g=0, x<>0],x);
{x = -Pi*_Z2}, {x = -Pi*_Z2}

There is information at

Random.Org that may interest you.
Thomas

From the help:
- a label e, using the syntax label=e. Essentially, labels are meant to distinguish several unspecified roots of the same equation.
So Maple is just indicating this information. If you want to see the solutions explicitly try this:
restart:
S:=[solve({x^2-y^2=y,2*x*y=x})];
op(3,S);
allvalues(%);
Hope this helps,
Thomas

If you use 2D input and do not execute each line after you type by using shift+return or arrow down your input will display like textbook notation. If you accidentally execute a line(s) go to the edit menu and choose remove output. I usually do all of this in document mode (Maple 10 or 11). I usually insert a table and put each question in its own block then you can then go back and generate and solution set very easily.
Thomas

I started using Maple at version 9.5 so I don't know.
I noticed that some of the people that would know have
missed the post so I am answering to bump it up to the
top. Hopefully they will take notice. If you don't
get a response I would repost it.
Thomas

Two methods that I can think of are:
Split the range of x (x=0..0.5 for area1, and x=0.5..1 for area2)
restart:
with(plots):
area1 := inequal({x>=0,y>=0,x+y<=0.5,y<=1},x=0..0.5,y=0..1,
optionsfeasible=(color=red),
optionsopen=(color=blue,thickness=2),
optionsclosed=(color=green, thickness=3),
optionsexcluded=(color=white)):
area2 := inequal({x<=1,y<=1,x+y>=1.5},x=0.5..1,y=0..1,
optionsfeasible=(color=yellow),
optionsopen=(color=blue,thickness=2),
optionsclosed=(color=green, thickness=3),
optionsexcluded=(color=white) ):
display([area1,area2]);
or you can make one set of inequalities and color in-between the lines.
area3 := inequal({x>=0,y>=0,x+y>=0.5,x+y<=1.5,x<=1,y<=1},x=0..1,y=0..1,
optionsfeasible=(color=red),
optionsopen=(color=blue,thickness=2),
optionsclosed=(color=green, thickness=3),
optionsexcluded=(color=white)):
display(area3);
Hope this helps,
Thomas

Avoid using the indexed name t[0]. For example
(1/m)*(int(b*t*(a-t), t = 0 .. T));
will work.
Thomas

There is some risk involved in using the following approach which JacquesC is more qualified to comment on than I am.
limit(sum((Pi+3*cos(n))/n, n = 1..k),k=infinity);
infinity
Thomas

I am not sure I understand your question but here are some things that might help. If you are trying to get random data from a particular distribution see the help Statistics[Sample]. Otherwise maple can generate many types of random objects. You can look at some of the following in the help: rand, RandomTools, RandomTools[Generate], randpoly, and these will lead you to links to others.
Hope this helps,
Thomas

You can put the data in a row Vector and use Statistics,Histogram (see Help), or you can go to the Tools->Assistants->Data Analysis. I would experiment with the assistant first, this will give you an idea how to manipulate the histogram if you do it directly from commands and options in the Statistics package.
Thomas

I think that the User Manual and Introductory Programming Guide are a great place to start. If you do not have hard copies, you can download PDF's from the main

Maplesoft site.
Additionally, if you post how to questions here you will find that the users are very helpful. I highly recommend the upgrade to Maple 11. I use Maple all of the time in the classroom for presentation. I also use the document mode to make test and handouts. If I had more say in the matter, I would try to get site license.
Hope this helps,
Thomas

Since it is strictly monotone and positive you could take the log.
f:=1/sqrt(k);
solve(diff(ln(f),k)<0,k);
RealRange(Open(0), infinity)
Thomas