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 a R script to construct a box plot showcasing the distribution of continuous variable grouped by a categorical variable using ggplot2's fill aesthetic

Implement a R program to create a histogram illustrating a distribution of a continous variable with overlays of density curves for each group using ggplot2.

Implement an R function to generate a line graph depicting the trend of time -series datasetb, with the separate lines for each group, utilizing ggplot2’s group aesthetic.

Write a R script to create a scatter plot, incorporating categorical analysis through color-coded data points representing different groups using ggplot2.

Develop a R programming to quickly explore agiven dataset including categorical analysis using the groups by command and visualize the findings using ggplot2 features.