A pet store sells dogs, cats, birds, and hamsters. Write a declaration for an anonymous enumerated data type that can represent the types of pets the store sells.

In C++, enumerations, or 'enums', serve as a way to group named integer constants that represent a set of related values. They make code more readable and understandable, by allowing developers to use descriptive names instead of numbers. An enum can be thought of as a custom data type that assigns names to integral constants.

Consider a scenario where you're writing a program for a pet store. You want to track different types of pets available. Instead of remembering that, say, '1' stands for dogs, '2' for cats, and so on, you can define an enumeration for pet types, and then use these named constants throughout your code. This approach reduces errors and improves code maintainability.

Programming with enums means using these sets of named values to make a program's source code more readable and to avoid the use of magic numbers. Once an enum is defined, you can declare variables of that enum's type and assign any of the enum's values to those variables.

For example, using the pet store's types of pets, once the enum is declared, you can create variables that can hold any pet type like so:
enum PetType { DOGS, CATS, BIRDS, HAMSTERS };
PetType myPet = DOGS;
This way, 'myPet' clearly indicates that it is of type 'PetType', and 'DOGS' represents an enumerated value from 'PetType'. Enums not only clarify the intended use of these variables but also enforce type safety, ensuring that only valid enumerated values are assigned to variables.

Data type declaration in programming defines a variable's type. It determines what kind of data the variable can hold and how much memory it will occupy. In C++, basic data types include 'int', 'char', 'float', and 'double'. Beyond these, developers can also define custom data types through structures, classes, and enumerations.

When declaring an anonymous enumerated data type, like in the pet store example, you detail the possible constant values without giving the enum a name. This is useful for one-off instances where the enumeration does not need to be reused elsewhere. The declaration looks like this:
enum { DOGS, CATS, BIRDS, HAMSTERS };
This declaration now allows variables to be defined with one of these four values, providing a clear context for what the variable represents.

C++ syntax encompasses the rules and guidelines that define how a C++ program is written and interpreted by the compiler. It covers how to declare variables, define functions, use operators, and structure the overall code among other things.

In the context of declaring an enumeration, the C++ syntax is straightforward: begin with the keyword 'enum', followed by an optional name, a list of enumerators enclosed within braces, and a concluding semicolon. It's crucial to write the code correctly; even a minor mistake, like missing a comma or semicolon, can result in compilation errors. Using correct syntax ensures that your program runs expectedly and also improves readability for yourself and others who may use your code.