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Two fundamental and troublesome problems seen in lower secondary mathematics classrooms are a limited understanding of the meaning of the equal sign, and a tendency to believe that a pronumeral such as x is an object rather than a quantity.
Hopefully some unexpected side effect of this will deal with the troublesome sin [phi] factor and allow the integral to be evaluated before I run out of different letters to use as pronumerals.
A pronumeral may represent a generalised number, a variable, a specific unknown or a parameter.
Consider the importance of distinguishing (even for advanced students) a handwritten multiplication symbol from a lower-case x, used as a pronumeral.