@hind 

restart;
u := x -> sin(x)+cos(x)-4*x+(alpha-4)*x:
v:=x->sin(x)-cos(x)+beta:
e1:=alpha - int(u(t)+v(t), t = 0 .. Pi):
e2:=beta - int(u(t)-v(t), t = 0 .. Pi):
s:=solve({e1,e2},{alpha,beta});

simplify(eval([e1,e2],s));

   [0,0]

@Christopher2222 

You have solved another system: a=0,b=0  instead of a=alpha,b=beta.

You may set e.g.

infolevel[fsolve]:=2;

to see what fsolve is doing. In your case it finally says "cannot converge to a solution".

You could try to restrict the domain, e.g. {a=0.5 .. 10,  ...}

@asa12 

You did not present your problem. It seems that you want to compute numerically some eigenvectors. But your problem has several parameters, and in order to obtain numerical results you should give numerical values to these parameters.

The expression is too complicated for a symbolic approach. Not to mention that for a symbolic approach it is better to avoid floating-point numbers.

@Axel Vogt 

d  is prime, otherwise the while loop would have stopped earlier!

@Markiyan Hirnyk 

If you think a bit, you will see that my code obtains the smallest odd prime.

@Markiyan Hirnyk 

n:=a(2015): d:=3: while irem(n,d)<>0 do d:=d+2 od: d;

      181

@Markiyan Hirnyk 

The A2 problem is simply not interesting from a Maple point of view because it can be solved instantly by brute force

(which is not the case with the rest of the problems).

@Markiyan Hirnyk 

This can be done by brute force.

a:=proc(n) option remember; 4*a(n-1)-a(n-2) end:
a(0):=1: a(1):=2:
ifactor(a(2015),easy);

@Earl 

plot3d deals only with surfaces. For a surface, even if closed, it could be very complicated/impossible to determine the "interior", see https://en.wikipedia.org/wiki/Alexander_horned_sphere

@hind 

You are pasting as text your 2d math expressions. This is not a good idea; it is better to upload the worksheet.

If you want to compute the integral j:

use

simplify(j) assuming x>0, x<Pi/2;

==>

@asa12 

eigenvector1[1] is a huge expression (its length is 280100). It is not a polynomial, so roundcoeffs1 cannot be used.

@Kitonum 

Yes, this seems to be the most concise solution (at least for a polynomial without parameters).

@Preben Alsholm 

round(a) is missing. This could be ok, but it is wrong for

p:=3.5*x^2+3.2*x-6.5+88.3*x*y-y^3+a*y + sin(1);

@schapplm 

I mean the inert form %arctan.

You can anytime use value(expr) to turn it into active.