Yes, the command is PDEtools:-difforder.

You need to explicitly put a multiplication symbol between x and y, and between 3 and x:

implicitplot(x^3+y^3-3*x*y=0,x=-3..3,y=-3..3, scaling=constrained);

Change and to a semicolon (;). Put a colon (:) or semicolon after the end do.

Acer's answer explains why your A3 doesn't work. I will explain why your A2 doesn't work. A2 will match expressions that literally contain `or` and whose left argument is integer and whose right argument is rational. (Since `or` will reject as erroneous any explicitly non-Boolean input such as numbers, this type can never be matched.)

Here's an example of a valid use of lowercase or as a type:

TypeTools:-AddType(A2, symbol or indexed):
type(y or s[2], A2);
     true
type(s[2] or y, A2);
     false

@smith_alpha 

Yes, I see your PS now. The output generated by "cmaple inputfile > outputfile" is not meant to be reread by a computer; it is strictly for human reading. If you are writing a file that is strictly meant to be reread by Maple, then the save command is by far the easiest way to do it: no formatting necessary and the reread values are automatically assigned to the correct variable names. Otherwise, use writedata or fprintf.

I think that you'd be better off using the command ImportMatrix, which understands the format "comma-separated values" through the parameter source= csv.

The assignment

x[anything]:= anything;

turns x into a table. Change x[s] to x_s or x__s.

A Horner-form for loop is probably the most efficient way, despite your distaste for it.

r:= rand();

L:= convert(r, base, 10):

S:= L[-1]: for k from 2 to nops(L) do S:= S*10+L[-k] end do: S;

     22424170465

However, there is also a library way to do it:

convert(L, base, 10, 10^nops(L))[];

     22424170465

N:= proc(m::posint)
local P:= 1, p:= 1, k;
     for k to m do
          p:= nextprime(p);
          P:= P*p
     end do;
     P+1
end proc:
M:= [$1..15]:
P:= N~([$1..15]):
SmallestPrimeFactor:= (n::posint)-> ifactors(n)[2,1,1]:
interface(rtablesize=16):
H:= < m | N[m] | S[m] | p[m] >:
<H, < <M[]> | <P[]> | <SmallestPrimeFactor~(P)> | <ithprime~(M)> >>;

You need to use diff consistently for derivatives. You correctly have diff(C(t), t) but expressions like d/dt and d*diff(n(t),t)/dt are meaningless. For a second derivative, use diff(n(t),t,t) or diff(n(t),t$2).

Yes, it is something simple. Don't use capital D as a variable. It is the functional differentiation operator.

restart:
assume(xi::real, eta::real):
phi:= (2*xi-1)*(xi-1)*(2*eta-1)*(eta-1):
Grad:= <diff(phi, xi), diff(phi, eta)>;

v:= <0,1>:
int(Grad.v, eta);

int(Grad.v, xi);

Hint: Continuity at  x = 0 means that the limit from the right and the limit from the left are equal and that these equal beta. In Maple, that means

limit(f, x= 0, left) = limit(f, x= 0, right);

This gives you an equation that you can solve numerically for alpha with the fsolve command.

Yes, you can manipulate inequalities exactly like equations. But three-part inequalities and three part equations are not allowed. Unfortunately, Maple will let you enter expressions such as (a<b) < c or (a=b) = c, but these operators are not associative! The expressions are essentially nonsense to Maple.

InertForm:-Display(InertForm:-Parse("2+3"));