C$++$ program with Mathematical Epressions :

A Mathematical epression is something like the following$2+(5*(3\mathrm{.}1^\{3\mathrm{.}3\}+$ sin$(6\mathrm{.}1)))/$ log$\_\{3\}(15)*2,$ in which there is a mixture of arithmetic expression, trigonometric, and logarithmic functions. Here is a list of those $12$ functions.

Basic arithmetic operators: $+,-,*,/$ along with the unary negation operator $-,$ i$.$e$.-5$

Unary scientific functions: sin$(),$ cos$(),$ tan$(),$ log$(),$ sqrt$()$

Binary scientific functions: log$\_\{$b$\}($a$)$ and $2^\{3\}.$ You should use the corresponding math functions in to implement them.

Remarks

Unary negation $-$: note that $-5^\{2\}$ must be interpreted as $-(5^\{2\})$ instead of $(-5)^\{2\}.$ The unary operator $-$ acts on any double and turns its value negative.

log$()$ stands for natural logarithm, i$.$e$.$ with base e $=2\mathrm{.}718....$

log$\_\{$b$\}($a$)$ is ordanry logarithm with base b$.$ Use the log$()$ function in to implement log$\_\{$b$\}($a$)$ as log$($a$)/$log$($b$).$

sqrt$()$ is square root.

$2^\{3\}$ stands for $2$ raising to the third power, which is equal to $8$

Note that, according to our syntax, the curly braces $\{\}$ are only used in logarithm$\text{'}$s subscript log$\_\{$b$\}($a$)$ and power's superscript $5\mathrm{.}1^\{2\}.$

The operators' priorities are listed as follows.

You do not need to check for invalid expressions $($like $2\mathrm{.}5+=3)$or invalid operations $($such as sqrt$(-5)).$

priority operators

lowest $+,-$

medium unary $-$

high $*,/$

highest sin$(),$ cos$(),$ tan$(),$ log$\_\{\}(),$ log$(),$ sqrt$(),^\{\}$

If two operators have the same priority, they should be evaluated in from left to right.

Write a class Expression that holds the value of a Mathematical epression and it has $($at least$)$ two member functions input$()$ and eval$(),$ in which the latter evaluates the expression. You may add members you like, as long as you keep all data members private or protected. We strongly suggest you use the getline$()$ function to read the whole expression as a stringobject $($remember to include $).$ Do not use cin $>>$ str; as it will stop on whitespaces. Use getline$($cin$,$ str$)$; instead to read the whole line $($in which str is a string object$).$ The main function is given as follows. Do not change main$()$ otherwise you may lose penalty points.