Here is the code:

class Exercises $\{$

$/**$ Returns the sum of the integers in given array. $*/$

public static int example$1($int$[]$ arr$)\{$

int n $=$ arr.length, total $=0$;

for $($int j$=0$; j $$ n; j$++)//$ loop from $0$ to n$-1$

total $+=$ arr$[$j$]$;

return total;

$\}$

$/**$ Returns the sum of the integers with even index in given array. $*/$

public static int example$2($int$[]$ arr$)\{$

int n $=$ arr.length, total $=0$;

for $($int j$=0$; j $$ n; j $+=2)//$ note the increment of $2$

total $+=$ arr$[$j$]$;

return total;

$\}$

$/**$ Returns the sum of the prefix sums of given array. $*/$

public static int example$3($int$[]$ arr$)\{$

int n $=$ arr.length, total $=0$;

for $($int j$=0$; j $$ n; j$++)//$ loop from $0$ to n$-1$

for $($int k$=0$; k j; k$++)//$ loop from $0$ to j

total $+=$ arr$[$j$]$;

return total;

$\}$

$/**$ Returns the sum of the prefix sums of given array. $*/$

public static int example$4($int$[]$ arr$)\{$

int n $=$ arr.length, prefix $=0,$ total $=0$;

for $($int j$=0$; j $$ n; j$++)\{//$ loop from $0$ to n$-1$

prefix $+=$ arr$[$j$]$;

total $+=$ prefix;

$\}$

return total;

$\}$

$/**$ Returns the number of times second array stores sum of prefix sums from first. $*/$

public static int example$5($int$[]$ first, int$[]$ second$)\{//$ assume equal$-$length arrays

int n $=$ first.length, count $=0$;

for $($int i$=0$; i $$ n; i$++)\{//$ loop from $0$ to n$-1$

int total $=0$;

for $($int j$=0$; j $$ n; j$++)//$ loop from $0$ to n$-1$

for $($int k$=0$; k j; k$++)//$ loop from $0$ to j

total $+=$ first$[$k$]$;

if $($second$[$i$]==$ total$)$ count$++$;

$\}$

return count;

$\}$

$\}$