How can I get single face without internal edges between circle and square?

When using the BRepAlgoAPI_Fuse operation on a circle and a square, I get the desired fused outcome, but the shape consists of two separate faces. The first being the full circle, and the second being the square minus the circle.

Is it possible to get only one face, so that I dont get the internal edge going between the two intersections of the fused shape?

CODE:
TopoDS_Face Face() {
TopoDS_Edge line = Line(gp_Pnt(0, 0, 0), gp_Pnt(8, 0, 0));
TopoDS_Edge line2 = Line(gp_Pnt(8, 0, 0), gp_Pnt(8, 8, 0));
TopoDS_Edge line3 = Line(gp_Pnt(8, 8, 0), gp_Pnt(0, 8, 0));
TopoDS_Edge line4 = Line(gp_Pnt(0, 8, 0), gp_Pnt(0, 0, 0));
TopoDS_Wire wire = BRepBuilderAPI_MakeWire(line, line2, line3, line4);
BRepBuilderAPI_MakeFace makeFace(wire, true);
return makeFace.Face();
}

TopoDS_Shape Circle() {
gp_Pnt centerPt(9, 9, 0);
gp_Dir dir(0, 0, -1);
gp_Ax2 ax2(centerPt, dir);
gp_Circ circ(ax2, 4);

Geom_Curve* curve = new Geom_Circle(circ);
BRepBuilderAPI_MakeEdge maker(curve);
BRepBuilderAPI_MakeWire wire(maker.Edge());
BRepBuilderAPI_MakeFace face(wire.Wire());
return face.Face();
}

TopoDS_Shape Fuse(TopoDS_Shape face1, TopoDS_Shape face2) {
BRepAlgoAPI_Fuse fuse(face1, face2);
fuse.SimplifyResult();
return fuse.Shape();
}