The calculator in Emacs has support for what it is you request, which it calls "interval forms". Interval form arithmetic simply means executing the operations in parallel on both ends of the interval.

It also has support for "error forms" which is close to what the calculator in OP uses. That takes a little more sophistication than just performing operations on the lower and upper number in parallel. In particular, the given points don't represent actual endpoints on a distribution, but rather low and high probability events. Things more or less likely than those can happen, it's just rare.

> I'm not especially good at stats

It shows! All the things you complain about make perfect sense given a little more background knowledge.

Is it actually just doing it at both ends or something nore complex? Because for example if I did 7 - (-1~2)^2 the actual range would be 3-7 but just doing both ends of the interval would give 3-6 as the function is maximised inside the range.