(Table of Squares and Cubes) Using only the programming techniques you learned in this chapter, write an application that calculates the squares and cubes of the numbers from 0 to 10 and prints the resulting values in table format, as shown below. [Note: This program does not require any input from the user.] $$\begin{array}{lll} \text { number } & \text { square } & \text { cube } \\ 0 & 0 & 0 \\ 1 & 1 & 1 \\ 2 & 4 & 8 \\ 3 & 9 & 27 \\ 4 & 16 & 64 \\ 5 & 25 & 125 \\ 6 & 36 & 216 \\ 7 & 49 & 343 \\ 8 & 64 & 512 \\ 9 & 81 & 729 \\ 10 & 100 & 1000 \end{array}$$

The Java for loop is a control structure that allows for concise iteration over a range of values, in this case, numbers from 0 to 10. In our exercise, the loop starts by initializing a variable named 'number' at 0 and it repeats the block of code inside until 'number' exceeds 10. The structure of the for loop typically includes initialization, condition, and an update statement, all encased within the loop syntax.
A simple illustration of the for loop used in the exercise looks like this:
for(int number = 0; number <= 10; number++) { // Code to calculate square and cube // Code to print the results}
In this syntax, 'int number = 0;' is the initialization, 'number <= 10;' is the condition to be met, and 'number++' is the update step. Notice how the loop controls the flow of execution, ensuring that the code to calculate and print the squares and cubes is performed for each number from 0 to 10.

Controlling a loop in Java means managing how and when the loop executes the code block defined within it. The for loop control is exhibited through three main segments: initialization, condition, and update. In our exercise context, loop control is crucial to accurately print the table of squares and cubes.

• Initialization: Setting up a variable before the loop starts, like 'int number = 0;'.
• Condition: The loop will continue to execute as long as this condition remains true, in this case 'number <= 10;'.
• Update: A statement that is executed after each iteration of the loop, often modifying the initialized variable, such as 'number++;'

Proper loop control ensures your program doesn't run indefinitely and that the logical progression of calculations is both orderly and efficient. The modification 'number++' increases the value of 'number' by 1 after each iteration, eventually leading to a false condition which exits the loop after printing the square and cube of 10.

In Java, arithmetic operations are used to perform mathematical calculations. The square of a number is found by multiplying the number by itself, and the cube is found by multiplying the square by the original number once more. These operations are performed using the multiplication '*' operator in Java.
Here's a breakdown of the arithmetic operations from the exercise:
int square = number * number; // Square calculationint cube = number * square; // Cube calculation
Arithmetic operations are not limited to multiplication; other operations include addition '+', subtraction '-', division '/', and modulus '%', which finds the remainder of division. By understanding and using arithmetic operations, you can perform a wide array of mathematical computations in Java, making it a powerful tool for building programs that require numeric calculations such as the one we see in our exercise.