How is a table (using your terminology, not Maple's table) different from a Matrix? Note that a Maple Matrix can have any type of generic data as its entries.

MyTable:= Matrix((10,2), fill= 0);

I just included the fill= 0 to be analogous to the Mathematica; it's actually the default. If you want to get fancy, you can also include the embedded assignments to n and m:

`&=`:= proc(n::evaln, v) assign(n,v); v end proc:   
MyTable:= Matrix((n &= 10, m &= 2), fill= 0);

(I wonder why Maple's assign doesn't already return the value. That would be so useful, and would make it more compatible with other languages.)

[I began posting this before Markiyan's Reply appeared. Sorry for any duplication.]

The radius of the sphere is 6, so your plot is completely inside the sphere. To see the sphere, you need to make the r range larger. You also need to switch theta and phi: In Maple's spherical coordinates the second coordinate is the longitude, and the third coordinate is the latitude.

plots:-implicitplot3d(
   (r*sin(theta)*cos(phi))^2+(r*sin(theta)*sin(phi))^2+(r*cos(theta))^2=36,
   r=-7..7, theta=0..2*Pi, phi=0..Pi, coords= spherical
);

I know it's a hack, but you can plot the components separately. This is similar to Kitonum's, but uses a single plot command and avoids piecewise.

F:= x-> 
   if not x::realcons then 'procname'(args) 
   elif abs(x) < 2 then x
   else undefined
   end if
:
plot(
   [F~([seq](x-n, n= -8..8, 4))[], [seq]([[n-2,-2],[n+2,2]][], n= -8..8, 4)],  
   x= -10..10, scaling= constrained, color= blue, style= [line$5, point], 
   symbol= circle, symbolsize= 16
);

Since you've been here on MaplePrimes many times before and the solution to this system is straightforward (no singularities, convergence issues, etc.), I wonder what difficulty you encountered.

restart:
Eq1:= 
   diff(F(eta),eta$4) - 
   M*(eta*diff(F(eta),eta$3) + 3*diff(F(eta),eta$2) + 
      diff(F(eta),eta)*diff(F(eta),eta$2) - F(eta)*diff(F(eta),eta$3)
   ) - 
   Ha^2*diff(F(eta),eta$2)
:
Eq2:= 
   diff(G(eta),eta$2) + 
   Pr*M*(F(eta)*diff(G(eta),eta) - eta*diff(G(eta),eta)) +
   Pr*Ec*diff(F(eta),eta$2)^2 + Nb*diff(H(eta),eta) + 
   diff(G(eta),eta) + Nt*diff(G(eta),eta)^2
:
Eq3:= 
   diff(H(eta),eta$2) + M*Sc*(F(eta)*diff(H(eta),eta) - eta*diff(H(eta),eta)) +
   Nt*diff(F(eta), eta, eta)/Nb
: 
IC1:= F(0) = 0, (D@@2)(F)(0) = 0, D(G)(0) = 0, D(H)(0) = 0:
IC2:= F(1) = 1, D(F)(1) = 0, G(1) = 1, H(1) = 1:
 
params:= {Ec = .1, Nt = .1, Nb = .1, Sc = .5, Pr = 10, M = .5}:
HA:= [0, 2, 4, 6, 8]:

for k to nops(HA) do
   P||k:= plots:-odeplot( 
      dsolve(eval({Eq||(1..3), IC||(1..2)}, params union {Ha= HA[k]}), numeric),
      [[eta, F(eta)], [eta, G(eta)], [eta, H(eta)]],
      linestyle= [1,2,3],
      color= [red, blue, green, black, purple][k]
   )
end do:
plots:-display(P||(1..nops(HA)));

There's a simple trick that let's you exploit the internal representation of an Array to get what you want:

[rtable_elems(DataName)[]];

How about

plots:-polarplot([[r, 0, r= 0..1], [r, Pi/6, r= 0..1]], color= magenta, thickness= 6);

How about

plot([seq(-arctan(2*m*x)/(1-x^2), m= 1..10)], x= 0..10, discont);

It is always dangerous and unreliable to expect terms or factors to appear in a certain order. Isn't the result that you want the same as would would get from simply simplify(dairihensu1)?

To list the first 10 prime Leyland numbers, use

select(isprime, {seq(seq(a^b+b^a, a= 2..99), b= 2..99)})[1..10];

Some guess work was required to come up with the 99; it's much larger than is needed, but Maple's integer arithmetic and primality testing are so fast that it doesn't matter. Note that putting integers into a set automatically sorts them.

Here's a one-line solution:

cnt:= Statistics:-Tally(op~([g[]]), output= table);

This produces table output, like Joe's.

Consider creating a Matrix with an initializer function, like this:

v:= Matrix((5,9), (i,j)-> F(V__dot[i], DD[j]));

where F represents any operation that you want. In your case, I think that you want

v:= Matrix((5,9), (i,j)-> V__dot[i]/(Pi/4)/DD[j]^2);

While entering the command, you should use Shift-Enter to get to the next line. Only use Enter when the command is complete. Thus, in the code portions of most worksheets, Shift-Enter would be more commonly used than Enter.

Download DirectSearch from the Maple Applications Center. I gave a more-complete Answer to your simultaneous Question on StackOverflow.

I'm on my mobile right now. I'll give your problem a more-thorough look when I get to a real computer. 

Use the solve command. See ?solve. If the equation is too complicated to solve symbolically, you can still get a numeric solution with fsolve if the equation has no symbolic parameters. 

A slightly ugly solution is to use $ in prefix form:

Array(`$`(1..3, n));

But, then again, everything is ugly in 2-D input, so maybe it doesn't matter. You should use 1-D input. To change your default format to 1-D input: Using the menus, do

• Tools => Options => Display => Input display => Maple Notation
• Interface => Default format for new worksheets => Worksheet
• Apply Globally.