Has Maple 11 changed the way you do mathematics?
For me, it has.
For me, Maple used to be a “mechanized mathematical assistant”. That is, when I was doing something mathematical, I would do it at my desk, with Maple on a computer beside me, to assist with some of the calculations. I used many sheets of paper; the papers were messy and disorganized. I would scribble equations, scratch out mistakes or recopy the good parts onto another sheet, have sub-results strewn about haphazardly, etc.
With Maple 11, things are different. Now I do mathematics almost entirely within Maple. Now I keep everything in a document. I type formulae with 2D input, which looks much like how I would write things on paper, except neater. Graphics are interwoven with the formulae (and can be scribbled on). Mistakes are erased within the document. Sub-results are nicely put into collapsible subsections. The organization can, and of course does, change as I figure things out.
And when I have an end result, the document has the derivation, already nicely written up and reasonably organized. The task of “writing it up in good”, which I find so tedious that I do not always do it (typically to my later regret), is largely already done. Now I just include a few more lines of text—quick and easy—and perhaps do a little more reorganizing.
Maplesoft has been making claims like the above for some years now, i.e. that Maple is a “mechanized mathematical environment”. I tried that with Maple before, but was not happy with it. With Maple 11, things are working much better. There are still some rough edges, but they are few. There is now a real improvement to my work environment and, consequently, my work process.