>restart:with(plots):
>r:=sin(3*t): 
>K:=30: for i from 1 to K do ti:=i*2*Pi/K:
>curve[i]:=polarplot(r(t), t=0..ti) od:
>display(seq(curve[i],i=1..K), insequence=true);

It was your choice of method.  LinearSolve is optimized for solving a set of linear equations.  I will let others who are more mathematically inclined than myself to comment on restricting the solution set.  Given x equations with x unknowns, there should be only one set of solutions to the given system, assuming a solution set exists.  You can take your vector of unknows and modifiy it in a loop to alter the contents of the vector by a certain amount, and repeatedly solve the system over and over to see what the outcomes look like. 

Look at the help pages for LinearAlgebra, specifically the LinearSolve command.  At the prompt, type the following and hit the enter key.  Take a look at the examples provided.  If it still does not work, post your worksheet, with the data files included.

>?LinearAlgebra[LinearSolve]

At the Maple prompt, type the following and hit the enter key.  This will bring up the help pages for the font styles that are available.  There is a section that shows how to modify or save an existing style so it is used by default in future worksheet sessions.

> ?worksheet/documenting/styles

For Windows OS,  create a file called maple.ini in the Users sub directory of your Maple installation.  There is already a file there called maple11.ini for my Maple 11 release.  In that maple.ini file, add the line

e:=exp(1):

and save the file.  That file will get loaded at start up every time you launch Maple.  Then if you execute ln(e), you will get 1 as an answer.  I tried it and it works.

Acer answers this question here:

Thank you for showing this.  I repeated your steps, and I got the table.  That's what was missing from the manual.  After doing this, my first thouhgt was, this is painful.  I much prefer Doug's method above.

I was not clear as to what  you wanted to do.  My appologies.  I have to rethink this, or you might want to post a link where we can download an example of what it is you are trying to do.  I saw your references earlier, but those were from a journal, and unless you have a subscription, you can not view the actual articles.

You can use the "display" function to combine as many plots as you like at once. See file below for an example.  It did not come out to well, as far as the plot of the function fitting the data, but it illustrates your question for overlaying one type of plot with another.

I would still like a step by step explanation (unlike what is available in the manual), to create a Table as shown in the help pages.  Once the document block is created and a Table is inserted, what exactly has to happen.  I tried various combinations of key clicks, but to no avail.  My results were not comprable to what was shown.  There are key steps missing.  Like I said earlier, the visual effects are pleasing, but I do not have the patience or the time to try to make something work just because it looks good.  Once I have the result I am looking for, I move on.  I wonder if the people who actually write the manuals are users of the program.  In this case, I imagine they are not.  Once I bring myselft to actually open the manual and read it, I expect things to work as documented step by step.

Just thinking out loud.

I think what Jacques is refering to can be found in the help pages for Maple Standard Interface (not Classic).  In version 11, typing the following will bring up the help page with examples:

>?worksheet,documenting,table

Scrolling half way down shows some nice examples.  Inserting the table can be done from the "Insert" menu.  There is an item called "Table..."

With all of that said, I have not figured out how to do this just yet, although I have downloaded some worksheets from Maplesoft that implement these tables.  I usually use the "Classic" interface, but some of the new features do look appealing.

 Agreed.  Old habits die hard.

I'm curious as to where your equation "a*sqrt(1-b*cos(Pi/(v+1)))" came from for the fit.  Using your initial values and plotting does not yield a nice fit to your data.  There are many ways to do this.  Here are some examples below.  Acer's post above addresses the issue with your warning  message.

>restart: with(plots): with(stats[statplots]):

>data:=[8, 12, 16, 20],[-4.725566456, -4.539439112, -4.482294752, -4.42732732];

>dataplot:=scatterplot(data,symbol=diamond,symbolsize=20,color=blue):

>dataplot;

>c1:=fit[leastsquare[[x,y],y=a+b*x+c*x^2,{a,b,c}]]([data]);

>c2:=fit[leastsquare[[x,y],y=a+b*x+c*exp(-x),{a,b,c}]]([data]);

>c3:=fit[leastsquare[[x,y],y=a+b*x+c*x^2+d*x^3,{a,b,c,d}]]([data]);

>lscurve1:=plot(rhs(c1),x=5..22,color=red):
>lscurve2:=plot(rhs(c2),x=5..22,color=green):
>lscurve3:=plot(rhs(c3),x=5..22,color=black):
>display(dataplot,lscurve1,lscurve2,lscurve3);

The following www.cs.uwaterloo.ca/~ecterrab/qft.html
might be of use to you.