Anti-derivative Gradient Field Visualization

Create a mathematical visualization showing the relationship between antiderivatives and a gradient field. First, draw a family of cubic curves in the coordinate plane, each represented by the equation x cubed divided by three plus a constant, with constants ranging from negative ten to ten in increments of zero point five, producing a series of vertically shifted parallel curves. Then, overlay a slope field based on the function x squared, using forty sample points to draw short line segments whose slopes match the value of x squared at each location. The final image should clearly illustrate how the curve family aligns with the slope field, aiding in the geometric understanding of derivatives.