Let \(\mathcal{R}\) be the circle centered at \((0,0)\) with radius 10. The lines \(x = 6\) and \(y=5\) divide \(\mathcal{R}\) 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 find \([\mathcal{R}_1] - [\mathcal{R}_2] - [\mathcal{R}_3] + [\mathcal{R}_4]\).
