Write a C$++$ program that performs the following: Prints on screen a selection menu as follow:

$1-$ Sin $($x$),$ Cos$($x$)$ and ex$.$

$2-$ Binary and Decimal.

$3-$ Factorial, power and Palindrome

$4-$ Count characters and print digits

$5-$ Exit

If user presses $1,$ the following sub menu should be displayed:$($call functions power and factorial to solve the following series.$)$

$1-$ Sin $($x$).$

$($Sin $($x$)=$x$-$x$^3/3!+$ x$/5!-/7!...."/$n$!)$

$2-$ Cos $($x$).$

$($Cos$($x$)=1-$x$/2+$ x$/4!-$x$/6!...$x$"/$n$!)3-$e$1+$x$/1!+$ x$/2+$ x$^2/3!...."/$n$!$

$4-$ Return to the main menu.

If user presses $2,$ program should call a function that displays the following sub$-$menu:

$1-$ Binary to Decimal: call a function that takes a binary number and convert it to decimal $2-$ Decimal to Binary: call a function that takes a decimal number and convert it to binary.

$3-$ Return to the main menu

If user presses $3,$ program should call a function that displays the following sub$-$menu.

$1-$ Find factorial of n$.$ call a function that finds the factorial of any number

$2-$ Find the power. $($x to the power n$).$ call a function that finds the power of x and n$.$

$3-$ Check if y is Palindrome number. call a function that takes integer x and checks if x is palindrome number or not.

$4-$ Return to the main menu

If user presses $4,$ program should call a function that displays the following sub$-$menu:

$1-$ Count characters.

$($Program should call a function that read a set of characters from the keyboard until q is pressed. The program should count the occurrence of each of these characters $($a$,$ e and r$).$

$2-$ Print digits: call a function that takes integer x and print its digits with separate spaces as $(1245)$ and print it as $(1245).$

$3-$ Return to the main menu.

To Exit press $5.$