In Maple 16  (obviously, the result must be positive):

VectorCalculus:-int(x+y, [x, y] = Sector(Ellipse((1/4)*x^2+(1/9)*y^2-1), 0, (1/2)*Pi));

                                                                        -2

Probably, this error occurs only in the latest versions, as in Maple 12 the output is correct. It would be interesting to know the reason for this behavior.

properties of operations on sets?

Example:

is((A minus B) intersect (A minus C) = A minus (B union C)) assuming A::set, B::set, C::set;

                                                                  FAIL

Contour lines must be ordinary circles. In fact, we get:

plots[contourplot](1/(x^2+y^2), x=-1..1, y=-1..1);

If we use the additional options, the result is even worse:

plots[contourplot](1/(x^2+y^2), x=-1..1,y=-1..1, numpoints=10000);

restart;

Vector([a, b]);  <a, b>;  # Identical results

a:=[1, 2]:  b:=[3, 4]:

Vector([a, b]), <a, b>;   # Different results. Why?

evalf(10.2^20, 50);

evalf((10+1/5)^20, 50);

Where are 50 digits of the first result?