Develop a function in R to plot a function curve based on a mathematical equation provided as input ,with different curve styles for each group ,using ggplot2.

Write an R script to construct a box plot showcasing the distribution of a continuous variable, grouped by a categorical variable, using ggplot2’s fill aesthetic.

Implement an R program to create HISTOGRAM illustrating the distribution of a continuous variable with overlays of density curves for each group using ggplot2.