test_defint = ->
  run_test [
    "defint(x^2,y,0,sqrt(1-x^2),x,-1,1)",
    "1/8*pi",

    # from the eigenmath manual

    "z=2",
    "",

    "P=[x,y,z]",
    "",

    "a=abs(cross(d(P,x),d(P,y)))",
    "",

    "defint(a,y,-sqrt(1-x^2),sqrt(1-x^2),x,-1,1)",
    "pi",

    # from the eigenmath manual

    "z=x^2+2y",
    "",

    "P=[x,y,z]",
    "",

    "a=abs(cross(d(P,x),d(P,y)))",
    "",

    "defint(a,x,0,1,y,0,1)",
    "3/2+5/8*log(5)",

    # from the eigenmath manual

    "x=u*cos(v)",
    "",

    "y=u*sin(v)",
    "",

    "z=v",
    "",

    "S=[x,y,z]",
    "",

    "a=abs(cross(d(S,u),d(S,v)))",
    "",

    "defint(a,u,0,1,v,0,3pi)",
    "3/2*pi*log(1+2^(1/2))+3*pi/(2^(1/2))",
  ]