@Carl Love I usually just cut them however I want.  Indeed the cutting is a little more difficult if you don't go all the way across but it doesn't matter for me, I would just cut close to the perpendicular point and then finish off with a hand saw.  Be neat to see both ways.  Which method would end up with a larger useable waste piece?  That is also of interest. 

In what context is the error related to?

Please post your example that caused the error.

@acap_619 What happens when you execute this line?  What is your output?

96*sin(2*beta*y)*cos(2*beta*y)*beta^4 + 96*sin(2*beta*y)*beta^4 ;

As Tom Leslie said any two of the sums on the lhs give solution except x and y together.  Both x and z and y and z provide solutions.  (Not trying to be cryptic, trying to be fast).  Something about adding the third which Maple has trouble, is it the y portion?  What if we separated the exp into something else?

@Joe Riel - ok I see, thanks. 

@Acer - thanks, I know you can't change the votes.  I mean what you found probably caused that person to remove his vote.  However that would be the only caveat with my method using macro. 

I don't believe I've ever seen anyone ever use macro before (*edit actually I found one other - but I don't see it often).

hmm, I did see an upvote, looks like you've altered his vote.  Unfortunately I didn't think about names going global.  Can it be fixed?  Does it work otherwise?

@acer to get around your p*v problem use parse and convert to string. 

The issue Acer presented below can be solved by converting to string and parsing.

restart;
macro(v^2=a^2+b^2):

p:=v:
p*v;
                  2
                 v

parse(convert(%,string))
                           2    2
                          a  + b

So Maple see's that v^2 has the value of a^2+b^2 but any variables that create v^2 are not linked to the macro v^2 (funny that v*v produces a^2+b^2 but p*v with p=v does not.  Is there anyway to link it?

Employing delayed evaluation would work here

('v²')²
               (a^2+b^2)²

@acer you are correct.  At first I thought it's what I wanted.  The macro would be missing some functionality that I might wish it to have. 

@Kitonum I understand the names idea (thanks) but it is not what I want.  My additional concepts answer above better explains what I would like.

probably right, maybe muddling concepts.   

@nm if v^2 is entered and you've created a value for v^2 then the output should be a^2+b^2.  However v^3 would be 125.  Although I can see where things would get confusing.

Now this is probably not a strong case but, back to the v^2 idea.  the value a^2+b^2 would be substituted anywhere in another equation where v^2 resides.  For example kinetic energy 1/2*m*v^2.

.. hm but then I guess we run into an automatic substitution when we might not want it. 

One good point is using v:=sqrt(a^2+b^2) where the value of v^2 is either + or - but using the v^2 assignment - it's already defined as positive. 

This is a good point.  From an aesthetical standpoint, a smooth thin line should appear for all higher values of numpoints, not some sweetspot number that makes the line appear good after which the line starts to appear thick and blocky. 

It appears the op is simply entering

plot(sin(x),numpoints=2000)

When entering numpoints=50000 I think it exagerates the point to why he is wondering why the lines aren't smooth.