# Part $($a$)-$ Function to count vowels in a word

def count$\_$vowels$($w$)$:

# Define the vowels

vowels $=$ 'aeiou'

# Initialize vowel count to $0$

vowel$\_$count $=0$

# Loop through each character in the word

for char in w:

# If the character is a vowel, increment the count

if char.lower$()$ in vowels:

vowel$\_$count $+=1$

return vowel$\_$count

# Part $($b$)-$ Function to estimate the number of syllables in a word

def count$\_$syllables$($w$)$:

# Define the vowels

vowels $=$ 'aeiou'

syllable$\_$count $=0$

# Check if the first character is a vowel and increment syllable count if so

if len$($w$)>0$ and w$[0].$lower$()$ in vowels:

syllable$\_$count $+=1$

# Loop through the string and check for non$-$vowel followed by a vowel

for i in range$(1,$ len$($w$))$:

if w$[$i$].$lower$()$ in vowels and w$[$i$-1].$lower$()$ not in vowels:

syllable$\_$count $+=1$

return syllable$\_$count

# Part $($c$)-$ Test cases

# Test cases for count$\_$vowels function

print$($count$\_$vowels$(\text{'}\text{'}))$ # $0$

print$($count$\_$vowels$(\text{'}$Z$\text{'}))$ # $0$

print$($count$\_$vowels$(\text{'}$sloth$\text{'}))$ # $1$

print$($count$\_$vowels$(\text{'}$SlOTh$\text{'}))$ # $1$

print$($count$\_$vowels$(\text{'}$slothy$\text{'}))$ # $1$

print$($count$\_$vowels$(\text{'}$ABACUS$\text{'}))$ # $3$

# Test cases for count$\_$syllables function

print$($count$\_$syllables$(\text{'}\text{'}))$ # $0$

print$($count$\_$syllables$(\text{'}$Z$\text{'}))$ # $0$

print$($count$\_$syllables$(\text{'}$i$\text{'}))$ # $1$

print$($count$\_$syllables$(\text{'}$OWL$\text{'}))$ # $1$

print$($count$\_$syllables$(\text{'}$tomato$\text{'}))$ # $3$

print$($count$\_$syllables$(\text{'}$write$\text{'}))$ # $2$