@Kitonum My method is only intended for VectorCalculus:-int integrals in rectangular coordinates, not for integrals "written in the usual way". Obviously you can see how it can be modified to handle the case that you present.

@Kitonum Thank you for bringing this situation to my attention. The following plotting command will handle such cases as well as the original case:

plots:-display(
    [seq](
        plot3d(0, op([1,2],j), op(2,j)),
        j= indets(J, Int(Int(algebraic, name= range(algebraic)), name= range(numeric)))
    ),
    orientation= [180, 0, 180]
);

@JanBSDenmark You can force use of real branches with the RealDomain package. You can also include x > 0 in the solve command:

solve({f(x) = 5., x > 0})

@Jjjones98 The notation Diraderivatrc(n,t) is described on the ?Dirac help page. It's a generalized derivative of Dirac(t).

@dharr The return values of Eigenvectors are a vector and matrix (both types of rtable). When nops is used on an rtable, it does not tell you the number of elements! Indeed, the result is usually 3. The command for the number of elements of an rtable is numelems. There were 4 eigenvalues and eigenvectors for both the cases that you reported as having 3. Since the eigenvectors are returned as a matrix, they can't be counted with numelems either. You need to count the nonzero columns of the matrix.

The command Eigenvalues works on all these examples, so there's no need to find the eigenvalues "the hard way". The problem only occurs when computing the eigenvectors.

@acer You wrote: 

• I'm also waiting for the world's infatuation with thin clients and the cloud to end.

This may not be what you meant by "the cloud", but I don't think that people will ever grow tired of being able to access their documents from nearly any computer/phone in the world.

A related question is What kind of symmetry, if any, is necessarily possessed by a quadrilateral that has both an inscribed circle and a circumscribed circle? Even something as symmetric as a nonsquare rectangle doesn't have an inscribed circle, so I'd guess that such quadrilaterals are quite rare.

The error message comes from lines 189-193 of 

showstat(LinearAlgebra:-LA_Main:-Eigenvectors)

when the computed dimension of the null space associated with a particular eigenvalue (aka the geometric multiplicity) is higher than was expected (i.e., the algebraic multiplicity). I suspect that this error can only happen when there are parameters.

@mmcdara Can you show that 3D error that you described? My 3D plot below has all tickmarks on all three axes modified without any problem.

@Kitonum A variation of that that works in 1D input is

'`>=`'(a, b) 

(That's single forward quotes (aka unevaluation quotes) on the outside and single backward quotes (aka name quotes) on the inside.) The prettyprinted output is in the standard infix form, without any quotes.

@Fzen If it's only the output form that matters to you, rather than changing a default, then you can use inert operators in prefix functional form. For example, the input

`%>`(a, b)

produces the output

a > b

and likewise for `%>=`.

Inert expressions can be converted to active form with the command value. 

@RLessard You wrote:

• The trick is to eliminate the term (2*i + 2*k)!  keeping only (2*i)!

Yes, that's exactly right. Once the factorial is thus reduced, each individual power series of the decomposition is immediately recognized as a variation of cos(x), and the more-complicated hypergeom representation is avoided.

@litun You wrote:

• As I know list is used for discrete parameters (natural numbers) and function for continuous parameters (real numbers).

That's not true. And not only is it not true, but in a Maple construction such as F[1,2](3.4), the [1,2] is not even a list; it's an index. A function's arguments (arguments is a better term than parameters in this context) can be placed in the index or in the main parentheses, but the reasons for choosing to put them in the index are mostly stylistic and have nothing to do with whether they are discrete or continuous. Index arguments are more difficult to program, and I recommend that you avoid them for now.

VV's Answer uses Maple 2019 syntax. 

@David Sycamore A symbol that looks similar to a stylized Greek phi is indeed a standard symbol for the empty set. Given that, {phi} represents the set that contains the empty set as its sole element, which is not the same thing as the empty set itself. If you're restricted to ASCII (plaintext) input, you can use { } unambiguously for the empty set, and this can also be used as Maple Input.