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For example when I make a new piece of content (or article, or page, or whatever the CMS calls it), I can add in my own HTML formatting and stuff, but when I try to add in php code it just spits it out as raw text.
The only CMS that I've found (that is free and open source anyway) that has an option to render a page with php code on it is Drupal. Am I right in assuming that the other CMS's simply can't/don't do this?
If you want to add your php code, you need to do this in the php files themselves. Most often, basic type php you want to add will go in the 'template', the 'style', or the 'theme'. Watch out for templates - not all of them allow php input.
This is all for some very good reasons - the basics of security in separation of coding and content, and sometimes the separation of code and design.
Some CMS's will allow you to add, via the browser, snippets of php which will be plopped somewhere on the page (using the php function eval()). This is frequently a bit of a gimmick, and not such a good idea security-wise; unless you trust the programmers implicitly, it's best to stay away from this kind of modules / blocks.