Verdict:
CalculationCenter works well for those who don't need the full weight of Mathematica and its ilk, most particularly for those who won't use it daily
Some things you can return to after weeks or years absence, picking them up as if you had last used them yesterday. Alas, this is not true of heavyweight maths packages such as Maple, Mathematica and Matlab. Each day that passes since you last used them pushes you a step back down their steep learning curves, until you're back where you started.
Wolfram's CalculationCenter is an acknowledgement that not all of us need a fully featured application, and that by making it easier to use, the learning curve is much less steep. You shouldn't have to pour over weighty tomes before you can start work. Indeed, its only printed documentation is a Getting Started pamphlet - after that there's excellent linked online assistance.
It's much easier to enter formulae: you can use command-key sequences to set exponents, employ spreadsheet text conventions such as (x^3)/(y^2), or let CalculationCenter suggest how to convert native Excel functions. Sadly, there's no support for TeX, still the most popular mathematical typesetting language, either as an import or export format.
If you're really struggling, you can use InstantCalculators to do almost everything for you. By default, a single Controller window offers button-based access to a range of related function helpers, which enable you to construct formulae, solve equations, plot functions, and export the results. Click on the button in the Controller, and it will embed an InstantCalculator dialog in your notebook (document), into which you insert the variable, formula and so on.
If you're unsure what to enter, or how to express it, click on the dialog's Show Example button to see what typical values can be inserted, and edit them yourself. As you become more proficient, you'll find you use InstantCalculators less, and direct entry more. Leave the package for a few months to work on something different, and you can rejoin it at any level of proficiency.
Hard
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graph
There are some rough edges that need improving. Select a mathematical formula and click on a relevant Controller button, and the formula will be automatically pasted into the dialog - very neat. However, if you select a graph and click on a relevant button, the new dialog will replace the graph altogether instead of making it the subject of the action. Given that CalculationCenter only has single-level undo, this inconsistency can be very harmful.
Indeed, trying to export a graph can be quite frustrating. Once you've learned that you mustn't click on the Export Graph As button with a graph selected, you'll find that the InstantCalculator dialog requires you to type in a file path, for example, 'Macintosh HD:Documents: MyFiles', and regenerate the graph by pasting in the formula or command anew. This use of explicit file paths again shows that the interface isn't thoroughly well designed, although luckily there's a menu command to use a 'get file' dialog to construct a text file path.
The calculation engine used is Mathematica Kernel version 4.1.4, which is a solid and proven semi-background application. It handles straight number-crunching, a useful range of statistics functions (new for this version), symbolic manipulation, complex numbers, eigenvalues and eigenvectors, and pretty well everything you're likely to require.
There's a lot of attention to detail: for example, the Open Special menu command helps you import files that do not use Mac character mappings. Surprisingly, there's not a fully Carbonized version to run native under Mac OS X, although it does work well in the Classic environment.
Calculated risk
In some ways, just as with Wolfram's flagship Mathematica itself, CalculationCenter is too self-centred. Apart from lack of support for TeX, you can't readily use it to typeset equations to be imported into other applications, although data can be moved freely using text files.
Its notebook documents can be formatted elegantly, and printed at high quality, as well as exported in HTML format. There's new and valuable support for MathML, which may ultimately supplant TeX.
All in all, CalculationCenter works well for those who don't need the full weight of Mathematica and its ilk, most particularly for those who won't use it daily. It's far superior to other middleweight packages such as MathCad, no longer offered for Mac anyway. With a little more attention to those rough edges, and an OS X version, it could steal the market.
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