+288 Let \(\mathcal{R}\) denote the circular region bounded by \(x^2+y^2=36\)\(.\) The lines \(x=4\) and \(y=3\) partition \(\mathcal{R}\) into four regions \(\mathcal{R}_1\)\(,\)\(\mathcal{R}_2,\)\(\mathcal{R}_3,\) and \(\mathcal{R}_4.\) Let \([\mathcal{R}_i]\) denote the area of region \(\mathcal{R}_i.\) If \([\mathcal{R}_1] > [\mathcal{R}_2] > [\mathcal{R}_3] > [\mathcal{R}_4]\)\(,\) then compute \([\mathcal{R}_1] - [\mathcal{R}_2] - [\mathcal{R}_3] + [\mathcal{R}_4].\)
