syms a b c x y s p q S
c=sqrt(((10+x)/sin(q))^2-x*x)
b=(10+x)/sin(q)
x=10*(sin(q)*(1-cos(p))-sin(p)*(1-cos(q)))/(sin(q)*(1-cos(p))+sin(p)*(1-cos(q)))
y=(10+x)/sin(q)-(10-x)/sin(p)
quad(@(s) (c*(b*b*2/3+x*x/3)-b*b*a+a*a*a/3-x*x*a+x*a*b*sin(q)-x*b*b*(asin(c/b)-pi/2+q)),pi,3,pi*3/2,[],[],cos(q)=2*(s^3)*(cos(160*pi/180)-cos(140*pi/180))/(pi^3)-3*(s^2)*(cos(160*pi/180)-cos(140*pi/180))/(pi^2)+cos(160*pi/180),p=q+pi)
c=sqrt(((10+x)/sin(q))^2-x*x)
b=(10+x)/sin(q)
x=10*(sin(q)*(1-cos(p))-sin(p)*(1-cos(q)))/(sin(q)*(1-cos(p))+sin(p)*(1-cos(q)))
y=(10+x)/sin(q)-(10-x)/sin(p)
quad(@(s) (c*(b*b*2/3+x*x/3)-b*b*a+a*a*a/3-x*x*a+x*a*b*sin(q)-x*b*b*(asin(c/b)-pi/2+q)),pi,3,pi*3/2,[],[],cos(q)=2*(s^3)*(cos(160*pi/180)-cos(140*pi/180))/(pi^3)-3*(s^2)*(cos(160*pi/180)-cos(140*pi/180))/(pi^2)+cos(160*pi/180),p=q+pi)
