To make your program more readable for help in the future, you  should use some indents. Allow me to make some changes in your program which I listed below. 

f:=x->x^3+6*x^2-11*x-10:
A:=1:
M:=0.0001:
E:=M+1:

while (A<>n) do
   A:=readstat("Would You Like To Find Another Root?[y/n](n to quit)"):

   if A=y then
      B:=readstat(`Initial Value One?`):
      C:=readstat(`Initial Value Two?`):
      if sign(f(B)) = sign(f(C)) then
           printf("No Roots In The Interval %a",[B,C]);
      else
           while E>M do
               d:=evalf((B+C)/2):
               #print('d'=d):
               print('f'(d)=f(d)):
               if   f(d)>0 and f(d)<f(C) then
                      C:=d;
                      E:=abs(f(d)):
               elif f(d)>0 and f(d)<f(B) then
                      B:=d:
                      E:=(abs(f(d))):
               elif f(d)<0 and f(d)>f(B) then
                      B:=d;
                      E:=(abs(f(d))):
               elif f(d)<0 and f(d)>f(C) then
                      C:=d:
                      E:=(abs(f(d))):
               elif f(d)=0                     then
                      E:=0:
               end if:
           end do:
      end if:   
      print(sol=evalf(d));
   end if:
end do:

Ken.Lin @ Taiwan

Refine the last line code to the codes listed below will serve your need.

> plist:=[]:
   for beta from 0 to 10 do
      fsolve({eq1,eq2}, {x,y});
      xx:=eval(x,%):
      yy:=eval(y,%%):
      plist:=[op(plist),[xx,yy,beta]]:
   end do:

  plist;
  plots[pointplot3d](plist,axes=boxed,symbol=solidcircle);

Ken.Lin @ Taiwan

For your reference,

Given with x+y=2 and s=z+y to get "s= z-x+2":

> isolate(x+y=2,y);
   algsubs(%,s=z+y);

Ken.Lin @ Taiwan

There are  many ways to draw a circle with given diameter, For example:

(1)By plottools[]...

    Oo:=[0,0]:
    P:=[1,1]:
    r:=Student[Precalculus][Distance](Oo,P);
    p1:=plottools[circle](Oo,r,color=red):
    plots[display](p1,scaling=constrained);

(2)By geometry[]...

    geometry[point](Oo,[0,0]):
    geometry[point](P,[1,1]):
    r:=geometry[distance](Oo,P);
    geometry[circle](c,[Oo,r]):
    geometry[draw](c,axes=normal);
 

I hope this will give some help.

Ken.Lin @ Taiwan

Use the combine() command ,not simplify().

For your reference:

sin(alpha)*cos(beta)+cos(alpha)*sin(beta):
%=combine(%);
sin(alpha)*cos(beta)-cos(alpha)*sin(beta):
%=combine(%);
cos(alpha)*cos(beta)+sin(alpha)*sin(beta):
%=combine(%);
cos(alpha)*cos(beta)-sin(alpha)*sin(beta):
%=combine(%);

Fun with Maple!

Ken.Lin @ Taiwan