In a similar vein, but without explicit indexing or raising to a power

tot := 0:
for d in convert(a,'bytes') do
     tot := 10*tot + d - 48;
end do:
tot;

In a similar vein, but without explicit indexing or raising to a power

tot := 0:
for d in convert(a,'bytes') do
     tot := 10*tot + d - 48;
end do:
tot;

For 2,

unwith(RealDomain):

use RealDomain in
   plot(x^(1/3), x = -1..1);
end use;

Another possibility is

with(RealDomain):
plot(x^(1/3), x = -1..1);

Note that Re(x^(1/3)) is incorrect, as you noticed.  It returns the real part of a complex root, which is different from the real root.

The reason is that Maple computes the principal value of the expression z^(1/3), which, for negative real z, lies in the upper right quadrant of the complex plane.  To see that, you may use conformalplot:

plots[conformalplot](z^(1/3), z = -1..1)

So far as the minus sign goes, that is, I believe, the en-dash in the Helvetica font. Not much can be done about that, except chose another font.

The position of the 0 (origin) is a bit weird. I assume that is because it is doing double-duty as the zero for both axes.  Aligning it vertically with the x-axis labels probably would be better. 

The suggestion in the help page seems reasonable to me; one can always use limit with the left or right option. How would you suggest evaluating an expression at a singularity?  Note, too, that the help page specifically mentions a singularity (not "discontinuity"); for example, one can do

y := sin(x)/x:
eval(y, x=0);
Error, numeric exception: division by zero
limit(y, x=0);
                   1

Here's a way to avoid a local operator

eval(map(`*`,a,'b'));

Here's a way to avoid a local operator

eval(map(`*`,a,'b'));

The introduction of parentheses as "programming indices" for rtables in Maple 12 precludes that application. See the help page ?rtable_indexing.

The introduction of parentheses as "programming indices" for rtables in Maple 12 precludes that application. See the help page ?rtable_indexing.

The following variations also work:

map(appy, M, x,y);
map(`?()`, M, [x,y]);

The following variations also work:

map(appy, M, x,y);
map(`?()`, M, [x,y]);

Notice the following discrepancy:

 q := (6*((1/3)*a-1/9))/(36*a-116+12*sqrt(12*a^3-3*a^2-54*a+93))^(1/3);
                                   6 (a/3 - 1/9)
            q := --------------------------------------------------
                                       3      2             1/2 1/3
                 (36 a - 116 + 12 (12 a  - 3 a  - 54 a + 93)   )
f1 := unapply(q,a);                                                         
                                     6 (1/3 a - 1/9)
         f1 := a -> --------------------------------------------------
                                          3      2             1/2 1/3
                    (36 a - 116 + 12 (12 a  - 3 a  - 54 a + 93)   )

f2 := a -> (6*((1/3)*a-1/9))/(36*a-116+12*sqrt(12*a^3-3*a^2-54*a+93))^(1/3);
                                     6 (1/3 a - 1/9)
        f2 := a -> ---------------------------------------------------
                                             3      2              1/3
                   (36 a - 116 + 12 sqrt(12 a  - 3 a  - 54 a + 93))
f1(1/3);
                                       0

f2(1/3);
Error, (in f2) numeric exception: division by zero

Using unapply caused a conversion from sqrt to an exponent of 1/2. 

Manipulating an exprseq can be tricky; you have to be careful when passing a sequence to a procedure because Maple then interprets it as separate arguments, which may not be what you want. Also, be careful when doing something like

exprseq := [a,b],[c,d]:
for elim in exprseq do ... end do;

This may not do what you want if the exprseq contains only one sublist, it will then "unpack" the list.