1. diff(x^3,x);
3*x^2

2. F(6)={[1,1,1,1,1,1],[1,1,1,1,2],[1,1,1,2,1],[1,1,2,1,1],[1,2,1,1,1],[2,1,1,1,1],[1,1,2,2],[1,2,1,2],[1,2,2,1],[2,1,1,2],[2,1,2,1],[2,2,1,1],[2,2,2]}

3. L2:=[op(L1),Mars]

We initialize WALKS(m,n) with either m or n or both negative to be the Empty set {} because the walks function only corresponds with positive steps, as there cannot be negative steps. It is also a recursive function, so this condition is the initial condition to prevent infinite regression.

We initialize WALKS(0,0) to be the singleton set {[]} because (0,0) means there is no movement, which is an empty walk. 

4. 
F:=proc(n) local F1,F2 :
option remember:
if n<0 then
  RETURN({}):
fi:
if n=0 then
  RETURN({[]}):
fi:
F1:=F(n-1):
F2:=F(n-2):
{seq([op(f1),1],f1 in F1),
seq([op(f2),2],f2 in F2)}:
end:

5. 
NuF:=proc(n) local F1,F2 :
option remember:
if n<0 then
  RETURN(0):
fi:
if n=0 then
  RETURN(1):
fi:
F1:=NuF(n-1):
F2:=NuF(n-2):
F1+F2:
end:

NuF(1000)=
70330367711422815821835254877183549770181269836358732742604905087154537118196933579742249494562611733487750449241765991088186363265450223647106012053374121273867339111198139373125598767690091902245245323403501

Maple complains if you try to do nops(F(1000)) because it exceeds the max number of computations.