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What algorithms does RM use in the trial / free version ?
The free version has all the same algorithmic capabilities as the advanced versions, the limitations are mainly around the amount of data that can be processed. There are native RapidMiner operators for many of these algorithms (Gradient Boosted Trees, Deep Learning, etc.) and in general any python or R algorithm would be available via the scripting extensions for those languages.
To complement what my sensei @Telcontar120 said: if you want to take a look at the RapidMiner operators, you just have to open RapidMiner Studio and see what is in the Operators panel. These are divided into Classification, Segmentation and others. Most of these are quite well documented on the Help panel, with example processes and exercises.
If these aren't enough (believe me, it takes a long way to find something that isn't there), you can find extensions to work with Keras, MonkeyLearn, Aylien and others, and there are two extensions to work with Python (I was able to make it work with the default Python installation from Mac, but believe me, you want Anaconda but you might haven't realized it yet), and R. The Marketplace is super easy to use.
All the best,