Random regression and classification problem generation with symbolic expression

For beginners in data science and machine learning, a common problem is to get hands on good, clean data set for quick practice. Regression and classification are two most common supervised machine learning tasks, that a practitioner of data science have to deal with. It is not always possible to get well-structured data set for practicing various algorithms that one learns. Now, Scikit-Learn, the leading machine learning library in Python, does provide random data set generation capability for regression and classification problems. However, the user have no easy control over the underlying mechanics of the data generation and the regression output are not a definitive function of inputs -- they are truly random. While this may be sufficient for many problems, one may often require a controllable way to generate these problems based on a well-defined function (involving linear, nonlinear, rational, or even transcendental terms).