I would like to solve an equation in the attached file as an exercise. I am looking for all solutions - including the complex ones. This is easily done using "derive". There are six solutions:

edited "test":

test.mw

Five are complex, and the single real solution can be guessed simply by taking a close look. I am unable to obtain the complete solution in Maple; I cannot find my mistake and would appreciate some advice.

The integral shown in the attached file "test" was posted on another forum for calculation. I unsuccessfully attempted to apply Green's theorem in Maple and—as befits a Maple beginner—failed. Does Maple offer a sequence of commands to carry this out? I would appreciate some advice. If this is possible, I would then tackle the line integral using the residue theorem.

Download test.mw

For exercises involving Pick's Theorem, I need grid points within a Cartesian coordinate system. How can "all" grid points - at least within the first quadrant - be generated without the tedious manual entry of integer coordinates? Is it possible to draw grid polygons as closed polylines simply by clicking on the grid points? (BTW: At the moment, this works well in the good old "Cabri.")
My search within the "Help" section (using terms such as plot, grid, mesh, lattice, etc.) proved unsuccessful.

For quite some time, I have wanted to solve the system attached in "test" using Maple. The smallest solution in natural numbers x, y, and z test.mw

Download test.mw

is known, and all these numbers are less than 4 × 10¹². Is this possible in Maple?

(x=1633780814400; y=252782198228; z=3474741058973)

...the essence of plane geometry is hidden within the following puzzle:
Given is a closed curve C. It is assumed to be non-self-intersecting, convex, and continuously differentiable everywhere (a closed Jordan curve). Let line segment AB be a chord of this curve, having a fixed length l. A point P lies on this chord at a fixed distance a from A and b from B, such that l = a + b. An orientation (or direction of circulation) is now assigned to the curve. The chord is then moved continuously along the closed curve in this assigned direction of circulation. As it moves, point P traces out a so-called locus curve O, which—upon completion of one full revolution of the chord—also forms a closed curve lying entirely within C.
The task is to calculate the area of ​​the region between C and O (i.e., the area lying inside C but outside O). Divide the result by the product of a and b, and then apply the "identify" function to the outcome.