The question in the title has been raised before over the years, but has maybe not received enough attention.
Reraising the question was motivated by a comment by Kitonum to a recent post on improved integration results in Maple 2016:
http://mapleprimes.com/maplesoftblog/202910-New-And-Improved-Integration-Results

Consider the following session.
restart;
assume(n=0);
n^2; #Returns n^2
eval(%);#Returns n^2
sin(n*Pi); # Returns 0
sin(n); # Returns sin(n)
eval(%); # Returns sin(n)
ln(n); #Returns ln(n)
ln(n*exp(1)); # Returns ln(n*exp(1))
expand(%); # Error, (in ln) numeric exception: division by zero
ln((n+1)*exp(1)); Returns ln((n+1)*exp(1))
expand(%); # Returns ln(n+1)+1
sqrt(n^2); # Returns 0
sqrt(n); # Returns n^(1/2)
eval(%,n=n^2); # Returns (n^2)^(1/2)
simplify(%); #Returns 0: simplify doesn't help in the examples above.
##################
We see that assume n=0 certainly doesn't imply that expressions always will be evaluated at n=0, but sometimes it appears that it does.
So what is the intended behavior when assuming equality?
##
Several years ago (Maple 14 or earlier) I overloaded assuming so that equality assumptions were handled by eval.
There was a discussion at the time in MaplePrimes about this. Shall try to find the link.

I recently got myself a 64 bit computer and have noticed that I cannot use the option compile=true in dsolve/numeric. Take the following simple example:

dsolve({diff(x(t),t)=x(t),x(0)=1},numeric,compile=true);
Error, (in dsolve/numeric/SC/preproc) unable to compile (rc=1), please try again, and if that fails verify your Windows compiler installation

I'm using Windows 10, but had the same problem with Windows 8.1 on the same machine.
The Compiler:-Compile examples in the help page all work.

What do I have to do to make the option compile=true work in dsolve/numeric?

You may safely assume that I don't know any technicalities about these things.

Which Maple versions will run on Windows 10? Windows 10 is offered free to users of Windows 7 and 8.1. Several (including old) Maple versions run on Windows 7.

It appears that email notifications have gone on Christmas vacation.
When will they be back?

What are the stopping criteria for fsolve?
I cannot find anything in the help page and there seems to be no way of adding an optional argument to fsolve about errors.

I was initially surprised by the results of the first two fsolve commands below:

restart;
infolevel[fsolve]:=2:
fsolve([x->1,x->3],[0.4,8]);
fsolve([x->1,x->3],[0..7,8..9]);
fsolve(x->1,0.4); #OK, returns unevaluated
fsolve([1,1],{x,y}); #OK, returns NULL

I assume that in the first two examples the criterion used is that at some point in the process the iterates [x(n+1),y(n+1)] and [x(n),y(n)] are close enough together and the difference between results from the two is small enough (clearly 0).