area and volume integrals with quadpack

A basic implementation which just uses quad_qags
(to be followed by functions which allow options):
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(%i2) load(qarea);

(%o2) "c:/work2/qarea.mac"
(%i3) qarea(x*y^2,[x,0,1],[y,0,1]);

(%o3) 0.16666666666667
(%i4) qarea(x*y^2,[x,0,1],[y,0,x]);

(%o4) 0.066666666666667
(%i6) qarea(x*y^2,[x,0,1],[y,0,1]);

(%o6) 0.16666666666667
(%i7) qarea(x*y^2,[x,0,1],[y,0,x]);

(%o7) 0.066666666666667
(%i8) qvolume(x*y^2*z^3,[x,0,1],[y,0,1],[z,0,1]);

(%o8) 0.041666666666667
(%i9) qvolume(x*y^2*z^3,[x,0,1],[y,0,x],[z,0,y]);

(%o9) 0.003968253968254

(%i10) qvolume(1/sqrt(x + y^2 + z^3),[x,0,1],[y,0,1],[z,0,1]);

(%o10) 1.088500610145352

(%i11) qarea(1+sin(5*x*y +y^2),[x,-1,1],[y,-sqrt(1-x^2),sqrt(1-x^2)]);

(%o11) 3.43677885014651

---------------------------------
code:

/* qarea.mac */

codelist : 
      [[1,"too many subintervals done"],
       [2,"excessive roundoff error detected"],
       [3,"extremely bad integrand behavior observed"],
       [4, "integration failed to converge"],
       [5, "integral is probably divergent or slowly convergent"],
       [6, "the input is invalid"]]$


 qgsz(ez,vz,vz1,vz2) := quad_qags(ez,vz,vz1,vz2)$
 
qarea(ex,uL,vL) :=
 block([u,u1,u2,v,v1,v2,rL,uverr],
      [u,u1,u2] : uL,
      [v,v1,v2] : vL,
       rL : qgsz(qgsz(ex,v,v1,v2)[1],u,u1,u2),
      if not listp(rL) then
            (print(" returns noun form "),return(false)),
      uverr : rL[4],
      if uverr = 0 then rL[1]
       else (print(" error = ",part(codelist,uverr,2)),
                  false))$
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Ted Woollett