Thanks, Stephen. Yes, something like what you report, '(no*solutions*exist)', is exactly the kind of thing that can go wrong. I'll catch that one, thanks.
Right now, only the existing commands are supported.
Sorry, using image results will happen at some point but it's not on the menu yet. Also, I'm not allowed legally to make all of Mathematica available, so there will be limits. (After all, this is an expensive program.) A user could write their own functions, *possibly* incl. plotting. But this would be a pretty manual process. That is, the framework wouldn't lend support to that yet, beyond allowing you to do a raw query and receive some XML result. Plots become image URLs. Which, of course, can be displayed on an HTML5 display! (Which ND1 happens to have.)
Good to hear you're liking what you see so far.
I found oneissue: integration limits are enforced to be numbers
(as in the 50g num integration command) when really this should allow for expressions (such as 2*pi).
New bug:"1.0beta1b": doing undo after using the "intelligent" ∫ command to do numerical integration doesn't restore the stack as expected.
The promised "how to extend the CAS" note is now available at http://forums.naivedesign.com/viewtopic.php?f=11&t=673