Eval module is one of my preferred modules. This module allows dynamic math functions being evaluated from text strings opening the road of many different options.
To start with this module here it is just little script using console for output:

[code=thinbasic]
USES "CONSOLE" '---We need Console module to write output
USES "EVAL" '---We need Eval module to evaluate math strings

DIM t0, t1 AS DOUBLE = TIMER '---Some timing variable
DIM MyFunction AS STRING '---Will contain math function to eval

'---Define Y = f(X) ... function
MyFunction = "y = COS(x) * 10 + SIN(x)"

'---Tells eval engine to define new 2 variables: x and y
Eval_SetNumber("x", 0)
Eval_SetNumber("y", 0)

'---Define a looper and its max
DIM Count AS LONG
DIM MaxCount AS LONG VALUE 50

FOR Count = -MaxCount to MaxCount
'---Set X value
Eval_SetNumber("x", Count)
'---Eval MyFunction
Eval(MyFunction)
'---Write some info output
CONSOLE_WRITELINE(format$(Count, "0000") & " " & Eval_GetNumber("y"))
NEXT

'---Measure the ending time
t1 = TIMER

'---Final results
CONSOLE_WRITELINE("------------------------------------------------------")
CONSOLE_WRITELINE("Time in seconds for " & str$(MaxCount * 2) & " loops: ")
CONSOLE_WRITELINE(FORMAT$(t1-t0, "#0.00000"))
CONSOLE_WRITELINE("------------------------------------------------------")

'---Wait for a key to stop execution
CONSOLE_WAITKEY
[/code]

More examples will come showing how to link script variable to Eval internal variables.
Also check about execution speed ...