I think Maple should emphasize occupational and problem specific packages, like its TA software for teachers. Maple should have a package or set of packages for each type of engineer: electrical,hydrological, etc. Actually, Maple should promote packages for all professions that tend to need it. An abundance of packages would enable many new users to benefit from the power of maple with the experience of the advanced users who helped develop the packages.

 Consider the sequence of divergent series in part evaluated by the following maple input.

f1 := seq((1-a)*(1/2)+sum((-1)^n*(n^(1/n)-a), n = 1 .. infinity), a = 1/10 .. 9*(1/10), 1/10): evalf(f1);

and

f2 := `$`((1-a)*(1/2)+sum((-1)^n*(n^(1/n)-a), n = 1 .. infinity), a = 2 .. 10): evalf(f2);

The Maple output, which is the MRB constant

See the following PDF for the geometry of the MRB constant.

http://www.marvinrayburns.com/what_is_mrb.pdf

If you have any questions, I would like to hear them.

Marvin Ray Burns

In the blog MRB Constant-D I noticed a peculiar outcome to several sets of equations involving f(n) = sin((a+b*floor(n))*Pi/M), where M is a constant to be explored, b is a number to be found and a is a "starting value" that causes f(n) ~=  -1, 0 or 1.

I want to report some progress in finding a closed-form for the MRB constant.

I found a sequence of closed-forms involving the MRB that gives "0." with interesting accuracy far beyond machine precision. To see it for yourself, simply plot 1 + Sin[Pi*(5060936308 + 78389363*Floor[n])/m],
where m is the MRB Constant, for n in any given domain. It is