Can you recommend a decent online or software calculator?

Essentially the most helpful is WolframAlpha, as Ami said, you can use your browser history here too.

WolframAlpha can carry out complex equations can comparisons much like a TI Calculator. Additionally they have some areas where you can see the simplification of an equation paired with charts and graphs where possible.

Personally, I always use Python's console.
It has history and allows all kinds of math operations.

It is available for Linux, Windows, Mac, ChromeOS, Android, and others.

A few people have mentioned Sage, but I think deserves a bit more of a plug. Firstly someone mentioned that Sage is quite large to install. This is true, the binary downolad comes in at around 1 gig, however you can use it for free online, without having to install a thing! Head on over to sagenb.org , and sign up for a free account, which will allow you to create and save your own worksheets. I think this is really nice--it feels like it's your "gmail" but for maths, so you can just log in from anywhere and "check your maths" if you want :-D

This is a very popular option--I believe that in the last 9 months around 30,000 people have created accounts! It's perfectly suited for high school students and undergraduates, since no installation is necessary, and hence it can be used straight away in any computer lab with internet access. Here's a screenshot of what the notebook looks like. (I just googled "sage notebook screenshot.") It's been designed to look and work like the Mathematica notebook system, and it's surprisingly slick and easy to use.

Sage screenshot http://sidk.info/wp-content/uploads/2007/11/sage_screenshot2.jpeg.

There really is a lot to recommend it. I used the online notebook for around 6 months before I installed a copy on my own computer, and this was because I became interested in developing Sage. Although Sage is based on Python (so in particular any Python syntax will work), you really don't need to know Python to get started using Sage--I didn't when I started.

Sage is quite powerful too. Aside from using Maxima for symbolic integration, I belive Sage uses Pari for highly optimised polynomial arithmatic, and I have used Sage for some pretty intense linear algebra computations (over the integers as well as over finite fields), although for this kind of thing you'll probably not want to rely on the online server which can be a little slow.

And let's not forget that you also get the moral boost of being part of something really positive--an movement to create an open source alternative to costly and "closed" alternatives like Mathematica, Maple and Matlab.

(Disclaimer: I just came back from the Sage Days 23 sage developers workshop in Leiden, and I'm a bit pumped!)

SpeQ is really nice. If you close it's left/right areas it's just like Notepad, but a Notepad which can compute stuff. You can change any line displayed, press Enter at it's end and the line will be recomputed.

Just like in Notepad, you can select any part of what's displayed and delete it. You can also paste non-mathematical text into it. It will also remember what's displayed inside it the next time you start it. It has an option to clear it's content on Exit.

A lot of people recommended Python. It's is my main programming language and I love it, but SpeQ it's MUCH more powerful and easy to use than Python as a calculator.

alt text http://dl.dropbox.com/u/190212/public/speq.png

http://www.speqmath.com/index.php?id=1

Google's calculator is very powerful: http://www.googleguide.com/help/calculator.html and your use history will be stored in your browser history.