Function illinois 

pub fn illinois<F>(
    f: F,
    a: &ExactNum,
    b: &ExactNum,
    tol: &ExactNum,
    p: usize,
    rm: RoundingMode,
    cc: &mut Consts,
) -> Option<ExactNum>
where
    F: FnMut(&ExactNum, usize, RoundingMode, &mut Consts) -> ExactNum,

Illinois (modified regula falsi) on [a, b].