Let G be a set on [-\(\pi\),\(\pi\) ] with Lebesgue measure \(| G| >0\) and let h(\(\theta)\) be a real function integrable on G. Define \[ T^*_ G(h(\theta))=\sup \int_{E}h(x)dx, \] where the superior is taken over all sets \(E\subset G\) with \(| E| =2\theta\). If \(G=[- \pi,\pi]\), then \(T^*_ G(h(\theta))=h^*(\theta)\), the Baernstein’s star-function. For any real \(\psi\), transfer \(G+\psi\) to be in [- \(\pi\),\(\pi\) ] by adding an integer time of \(\pi\). G is said to be symmetric if \[ T^*_{G+\psi}(\cos \theta)\leq T^*_ G(\cos \theta). \] Let S be the class of functions \(f(z)=z+..\). regular and univalent in \(| z| <1\), and P be the class of functions \(p(z)=1+..\). regular and having positive real part in \(| z| <1\). If G is a symmetric set and if \(\phi\) (t) is a nondecreasing convex function on \(-\infty <t<\infty\), the author proves that the maximum of the integral \[ \int_{G}\phi (\log | f^{(m)}(re^{i\theta})|)d\theta,\quad f\in F,\quad 0<r\leq 1, \] is attained for a certain extremal function in F, provided that F is one of the following subclasses of S: (a) starlike functions, (b) convex functions, (c) close-to-convex functions, and that F is P or is the class of typically-real functions.