Is there a simpler and more elegant way to get the last result in this code snippet?

add(f~([op(a+b)])[]);
                          f(a) + f(b)
# simpler and more elegant
map(f, a+b);
                          f(a) + f(b)
# now I want to obtain this result
add(f~([op(a+b)], t)[]);
                       f(a, t) + f(b, t) 

TIA

Hi, 
I met a an unexpected behaviour of a procedure when the parameter sequence contains the type ':-RandomVariable':  

restart:
with(Statistics):
f1 := proc(A::':-RandomVariable')
  Mean(A)
end proc:

Z := RandomVariable(Normal(mu, sigma)):
hastype(Z, ':-RandomVariable');
f1(Z)
                              true
Error, invalid input: f1 expects its 1st argument, A, to be of type 'RandomVariable', but received _R
# Another attempt
f2 := proc(A)
  if hastype(A, ':-RandomVariable') then Mean(A) end if;
end proc:

f2(Z)
                               mu

Why does f1 generate this error?

Type_RandomVariable.mw

Version used MAPLE 2015.2

I use dualaxisplot and want a logarithmic horizontal axis.
I can get the expected graphic using either of these two methods

restart:
with(plots):
dualaxisplot(
  plot(x, x=0..1, color=blue, axis[1]=[mode="log"]),
  plot(1-x, x=0..1, color=red, axis[1]=[mode="log"]),
  gridlines=true
):

dualaxisplot(
  semilogplot(x, x=0..1, color=blue),
  semilogplot(1-x, x=0..1, color=red),
  gridlines=true
):

This worksheet contains my true code
(pink lines correspond to < plot + axis[1]=[mode="log"] > and blue lines to < semilogplot >).
You will see that the vertical axis for the plot declared in second position is logarithmic, whatever the way the logarithmic x-axis is defined. 
DecisionProb.mw

I am unable to find out if I made a mistake (which is likely) or if it is a bug?
Could you please have a look at this code and give me an answer?
Thanks in advance

I recently got stuck on a strange behavior of odeplot which did not return any result (only the axes were drawn).
Convinced that the solution of the differential system was correctly constructed, I noticed that drawing it, without using odeplot, gave me the correct result.
I then discovered that the range option (which I mistakenly defined) was the cause.

But this led me to the following question: what does this option really do?

Here is a notional example. The two questions are at the end of the worksheet.
 

Download The_role_of_range.mw

Please note that the last couple of commands strangely overpasses the < Warning, cannot evaluate the solution further right of 2.2825424, event #1 triggered a halt > limitation.

I incidently^(*) discovered that using MatrixPower to find the square root matrix of a relatively small matrix, returns wrong results, even for symetric positive definite matrices.

Trying to understand how MatrixPower proceeds using showstat is not that easy, but something I'm almost sure is that it doesn't ise an Eigenvectors decomposition.

Here is an example where I'm seeking for a matrix M such that C = M^2 and C is symetric definite positive of dimension 40.
(I didn't check if problems already occurs for smaller sizes)

^(*)  I was very bored by the prohibitive execution time of MatrixPower and looked for an alternative.

The matrix M that MatrixPower generates is far from verifying C = M^2 (using the option 'shape'='symmetric' doesn't improve anything).
The naive alternative based on an Eigenvectors decomposition works perfectly well while being 200 times faster.

Download MatrixPower_bug.mw